Wikipedia - User contributions [en]

Smale's problems

2016-05-23T08:26:23Z

Beltranc:

'''Smale's problems''' are a list of eighteen [[unsolved problems in mathematics]] that was proposed by [[Stephen Smale|Steve Smale]] in 1998,<ref>{{cite journal | first = Steve | last = Smale|title = Mathematical Problems for the Next Century|journal = Mathematical Intelligencer|year =1998|volume=20|number=2|pages=7–15|id = {{citeseerx|10.1.1.35.4101}}|doi=10.1007/bf03025291}}</ref> republished in 1999.<ref>{{cite book | first = Steve | last = Smale |editor1-first = V. I. | editor1-last = Arnold | editor2-first = M. | editor2-last = Atiyah | editor3-first = P. | editor3-last = Lax | editor4-first = B. | editor4-last = Mazur | title=Mathematics: frontiers and perspectives |publisher=American Mathematical Society|year=1999|pages=271–294 |chapter=Mathematical problems for the next century|isbn=0821820702}}</ref> Smale composed this list in reply to a request from [[Vladimir Arnold]], then vice-president of the [[International Mathematical Union]], who asked several mathematicians to propose a list of problems for the 21st century. Arnold's inspiration came from the list of [[Hilbert's problems]] that had been published at the beginning of the 20th century.

== List of problems ==

{| class="wikitable"
! #
! width="40%"| Formulation !! Status
|-
|style="text-align: center"| 1
| [[Riemann hypothesis]] (see also [[Hilbert's eighth problem]])
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 2
| [[Poincaré conjecture]]
| Proved by [[Grigori Perelman]] in 2003 using [[Ricci flow]].<ref>{{cite arXiv | last = Perelman | first = Grigori | authorlink = Grigori Perelman | title = The entropy formula for the Ricci flow and its geometric applications | eprint = math.DG/0211159 | year = 2002 | class = math.DG }}</ref><ref>{{cite arXiv | last = Perelman | first = Grigori | title = Ricci flow with surgery on three-manifolds | eprint = math.DG/0303109 | year = 2003 | class = math.DG }}</ref><ref>{{cite arXiv | last = Perelman | first = Grigori | title = Finite extinction time for the solutions to the Ricci flow on certain three-manifolds | eprint = math.DG/0307245 | year = 2003 | class = math.DG }}</ref>
|-
|style="text-align: center"| 3
| [[P = NP problem|Does P = NP?]]
|
|-
|style="text-align: center"| 4
| Shub–Smale τ-conjecture on the integer zeros of a polynomial of one variable<ref>{{cite journal | last1=Shub | first1=Michael | last2=Smale | first2=Steve | title=On the intractability of Hilbert’s Nullstellensatz and an algebraic version of "NP≠P?" | zbl=0882.03040 | journal=Duke Math. J. | volume=81 | pages=47–54 | year=1995 | doi=10.1215/S0012-7094-95-08105-8 }}</ref><ref>{{cite book | last1=Bürgisser | first1=Peter | title=Completeness and reduction in algebraic complexity theory | zbl=0948.68082 | series=Algorithms and Computation in Mathematics | volume=7 | location=Berlin | publisher=[[Springer-Verlag]] | year=2000 | isbn=3-540-66752-0 | page=141 }}</ref>
|
|-
|style="text-align: center"| 5
| Height bounds for [[Diophantine equation|Diophantine curve]]s
|
|-
|style="text-align: center"| 6
| Finiteness of the number of relative equilibria in celestial mechanics
| Proved for five bodies by A. Albouy and V. Kaloshin in 2012.<ref>{{cite journal | first1 = A. | last1 = Albouy | first2 = V. | last2 = Kaloshin |title= Finiteness of central configurations of five bodies in the plane |journal=[[Annals of Mathematics]] |volume= 176 |year=2012 |pages=535–588 |doi=10.4007/annals.2012.176.1.10}}</ref>
|-
|style="text-align: center"| 7
| Distribution of points on the 2-sphere
| A noteworthy form of this problem is the [[Thomson Problem]] of equal point charges on a unit sphere governed by the electrostatic [[Coulomb's law]]. Very few exact N-point solutions are known while most solutions are numerical. Numerical solutions to this problem have been shown to correspond well with features of [[Electron configuration|electron shell-filling]] in [[Atomic structure]] found throughout the [[periodic table]].<ref>{{cite journal | first = T., Jr | last = LaFave |title= Correspondences between the classical electrostatic Thomson Problem and atomic electronic structure |url=http://www.pagesofmind.com/FullTextPubs/La13-LaFave-2013-Correspondences-between-the-Thomson-Problem-and-Atomic-Structure.pdf|accessdate= 11 Feb 2014| journal=Journal of Electrostatics |volume= 71 |issue=6 |year=2013 |pages=1029–1035|doi=10.1016/j.elstat.2013.10.001}}</ref> A well-defined, intermediate step to this problem involving a point charge at the origin has been reported.<ref>{{cite journal |first = T., Jr | last = LaFave |title= Discrete transformations in the Thomson Problem |url=http://www.pagesofmind.com/FullTextPubs/La14-LaFave-2014-Discrete-Transformations-in-the-Thomson-Problem.pdf|accessdate= 11 Feb 2014| journal=Journal of Electrostatics |volume= 72 |issue=1 |year=2014 |pages=39–43|doi=10.1016/j.elstat.2013.11.007}}</ref>
|-
|style="text-align: center"| 8
| Extend the mathematical model of [[general equilibrium theory]] to include [[price]] adjustments
|Gjerstad (2013) <ref>{{cite journal | first = Steven | last = Gjerstad |title= Price Dynamics in an Exchange Economy |url=http://link.springer.com/article/10.1007%2Fs00199-011-0651-5| journal=Economic Theory |volume= 52 |issue=2 |year=2013 |pages=461–500|doi=10.1007/s00199-011-0651-5}}</ref> extends the deterministic model of price adjustment to a stochastic model and shows that when the stochastic model is linearized around the equilibrium the result is the autoregressive price adjustment model used in applied econometrics. He then tests the model with price adjustment data from a general equilibrium experiment. The model performs well in a general equilibrium experiment with two commodities.
|-
|style="text-align: center"| 9
| The [[linear programming]] problem: find a [[Time complexity#Strongly and weakly polynomial time|strongly-polynomial time]] algorithm which for given matrix ''A'' ∈ '''R'''''m''×''n'' and ''b'' ∈ '''R'''''m'' decides whether there exists ''x'' ∈ '''R'''''n'' with ''Ax'' ≥ ''b''.
|
|-
|style="text-align: center"| 10
| [[Pugh's closing lemma]] (higher order of smoothness)
|
|-
|style="text-align: center"| 11
| Is one-dimensional dynamics generally hyperbolic?
| Smale states two variants of this problem: the complex-variable one ("Can a complex polynomial {{math|''T''}} be approximated by one of the same degree with the property that every critical point tends to a periodic sink under iteration?") and the real-variable version ("Can a smooth map {{math|''T'': [0,1] → [0,1]}} be {{math|''C''''r''}} approximated by one which is hyperbolic, for all {{math|''r'' > 1?}}"). The former remains open even in the simplest parameter space of polynomials, the [[Mandelbrot set]]. The latter was proved by Kozlovski, Shen and van Strien<ref>{{cite journal | first1 = O. | last1 = Kozlovski | first2 = W. | last2 = Shen | first3 = S. | last3 = van Strien |title= Density of hyperbolicity in dimension one|journal=[[Annals of Mathematics]] |volume= 166 |year=2007 |pages=145–182 |doi=10.4007/annals.2007.166.145}}</ref> in 2007.
|-bgcolor="99FF99"
|style="text-align: center"| 12
| [[Centralizer and normalizer|Centralizers]] of [[diffeomorphism]]s
| Solved in the C1 topology by C. Bonatti, S. Crovisier and [[Amie Wilkinson]]<ref>{{cite journal | first1 = C. | last1 = Bonatti | first2 = S. | last2 = Crovisier | first3 = A. | last3 = Wilkinson |title= The C1-generic diffeomorphism has trivial centralizer |journal=[[Publications Mathématiques de l'IHÉS]] |volume= 109 |year=2009 |pages=185–244 |doi=10.1007/s10240-009-0021-z}}</ref> in 2009.
|-
|style="text-align: center"| 13
| [[Hilbert's sixteenth problem|Hilbert's 16th problem]]
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 14
| [[Lorenz attractor]]
| Solved by [[Warwick Tucker]] in 2002 using [[interval arithmetic]].<ref>{{cite journal | first = Warwick | last = Tucker |title=A Rigorous ODE Solver and Smale's 14th Problem |journal=Foundations of Computational Mathematics |volume=2 |issue=1 |year=2002 |pages=53–117 |doi=10.1007/s002080010018 |url=http://www.math.cornell.edu/~warwick/main/rodes/JFoCM.pdf}}</ref>
|-
|style="text-align: center"| 15
| Do the [[Navier–Stokes equations]] in '''R'''3 always have a [[Navier–Stokes existence and smoothness|unique smooth solution]] that extends for all time?
|
|-
|style="text-align: center"| 16
| [[Jacobian conjecture]]
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 17
| Solving [[polynomial equations]] in [[P (complexity)|polynomial time]] in the average case
| C. Beltrán and L. M. Pardo found a uniform probabilistic algorithm (average [[Las Vegas algorithm]]) for Smale's 17th problem <ref>{{cite journal | first1 = Carlos | last1 = Beltrán | first2 = Luis Miguel | last2 = Pardo |title= On Smale's 17th Problem: A Probabilistic Positive answer |journal=Foundations of Computational Mathematics |volume=8 |issue=1 |year=2008 |pages=1–43 |doi=10.1007/s10208-005-0211-0 |url=http://personales.unican.es/beltranc/archivos/Smale17FoCM.pdf}}</ref><ref>{{cite journal | first1 = Carlos | last1 = Beltrán | first2 = Luis Miguel | last2 = Pardo |title= Smale's 17th Problem: Average Polynomial Time to compute affine and projective solutions|journal=Journal of the American Mathematical Society|volume=22 |year=2009 |pages=363–385|url=http://personales.unican.es/beltranc/archivos/AffSmale17JAMS.pdf |doi=10.1090/s0894-0347-08-00630-9}}</ref> F. Cucker and P. Bürgisser made the [[smoothed analysis]] of a probabilistic algorithm ''à la Beltrán-Pardo'', and then exhibited a deterministic algorithm running in time <math>N^{O(\log\log N)}</math> <ref>{{cite journal | first1 = Felipe | last1 = Cucker | first2 = Peter | last2 = Bürgisser |title= On a problem posed by Steve Smale|journal=[[Annals of Mathematics]] |volume=174 |issue=3|year=2011 |doi=10.4007/annals.2011.174.3.8 |pages=1785–1836}} </ref>. Finally, P. Lairez found an alternative method to de--randomize the algorithm and thus found a deterministic algorithm which runs in average polynomial time<ref>{{cite journal | first1 = Pierre | last1 = Lairez |title= A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time |journal=Foundations of Computational Mathematics |volume=to appear |year=2016 }}</ref>. The problem is now considered as fully solved. All these works follow Shub and Smale's foundational work (the "Bezóut series") started in <ref>{{cite journal | first1 = Michael | last1 = Shub | first2 = Stephen | last2 = Smale |title= Complexity of Bézout's theorem. I. Geometric aspects |journal=J. Amer. Math. Soc. |volume=6 |issue=2 |year=1993 |pages=459-501 |doi=10.2307/2152805}}.</ref>
|-
|style="text-align: center"| 18
| Limits of [[intelligence]] (It talks about the fundamental problems of intelligence and learning, both from the human and machine side)<ref>http://recursed.blogspot.jp/2006/02/tucson-day-3-interview-with-steve.html Friday, February 03, 2006 Tucson - Day 3 - Interview with Steve Smale </ref>
|
|}

Smale also listed three additional problems:<ref>{{cite journal | first = Steve | last = Smale|title = Mathematical Problems for the Next Century|journal = Mathematical Intelligencer|year =1998|volume=20|number=2|pages=7–15|id = {{citeseerx|10.1.1.35.4101}}|doi=10.1007/bf03025291}}</ref>
#[[Mean value problem]]
#Is the [[three-sphere]] a [[minimal set]]?
#Is an [[Anosov diffeomorphism]] of a [[compact manifold]] topologically the same as the [[Lie group]] model of John Franks?

== See also ==
* [[Millennium Prize Problems]]

== References ==
{{reflist|2}}

[[Category:Unsolved problems in mathematics]]

Smale's problems

2016-05-23T08:13:02Z

Beltranc:

'''Smale's problems''' are a list of eighteen [[unsolved problems in mathematics]] that was proposed by [[Stephen Smale|Steve Smale]] in 1998,<ref>{{cite journal | first = Steve | last = Smale|title = Mathematical Problems for the Next Century|journal = Mathematical Intelligencer|year =1998|volume=20|number=2|pages=7–15|id = {{citeseerx|10.1.1.35.4101}}|doi=10.1007/bf03025291}}</ref> republished in 1999.<ref>{{cite book | first = Steve | last = Smale |editor1-first = V. I. | editor1-last = Arnold | editor2-first = M. | editor2-last = Atiyah | editor3-first = P. | editor3-last = Lax | editor4-first = B. | editor4-last = Mazur | title=Mathematics: frontiers and perspectives |publisher=American Mathematical Society|year=1999|pages=271–294 |chapter=Mathematical problems for the next century|isbn=0821820702}}</ref> Smale composed this list in reply to a request from [[Vladimir Arnold]], then vice-president of the [[International Mathematical Union]], who asked several mathematicians to propose a list of problems for the 21st century. Arnold's inspiration came from the list of [[Hilbert's problems]] that had been published at the beginning of the 20th century.

== List of problems ==

{| class="wikitable"
! #
! width="40%"| Formulation !! Status
|-
|style="text-align: center"| 1
| [[Riemann hypothesis]] (see also [[Hilbert's eighth problem]])
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 2
| [[Poincaré conjecture]]
| Proved by [[Grigori Perelman]] in 2003 using [[Ricci flow]].<ref>{{cite arXiv | last = Perelman | first = Grigori | authorlink = Grigori Perelman | title = The entropy formula for the Ricci flow and its geometric applications | eprint = math.DG/0211159 | year = 2002 | class = math.DG }}</ref><ref>{{cite arXiv | last = Perelman | first = Grigori | title = Ricci flow with surgery on three-manifolds | eprint = math.DG/0303109 | year = 2003 | class = math.DG }}</ref><ref>{{cite arXiv | last = Perelman | first = Grigori | title = Finite extinction time for the solutions to the Ricci flow on certain three-manifolds | eprint = math.DG/0307245 | year = 2003 | class = math.DG }}</ref>
|-
|style="text-align: center"| 3
| [[P = NP problem|Does P = NP?]]
|
|-
|style="text-align: center"| 4
| Shub–Smale τ-conjecture on the integer zeros of a polynomial of one variable<ref>{{cite journal | last1=Shub | first1=Michael | last2=Smale | first2=Steve | title=On the intractability of Hilbert’s Nullstellensatz and an algebraic version of "NP≠P?" | zbl=0882.03040 | journal=Duke Math. J. | volume=81 | pages=47–54 | year=1995 | doi=10.1215/S0012-7094-95-08105-8 }}</ref><ref>{{cite book | last1=Bürgisser | first1=Peter | title=Completeness and reduction in algebraic complexity theory | zbl=0948.68082 | series=Algorithms and Computation in Mathematics | volume=7 | location=Berlin | publisher=[[Springer-Verlag]] | year=2000 | isbn=3-540-66752-0 | page=141 }}</ref>
|
|-
|style="text-align: center"| 5
| Height bounds for [[Diophantine equation|Diophantine curve]]s
|
|-
|style="text-align: center"| 6
| Finiteness of the number of relative equilibria in celestial mechanics
| Proved for five bodies by A. Albouy and V. Kaloshin in 2012.<ref>{{cite journal | first1 = A. | last1 = Albouy | first2 = V. | last2 = Kaloshin |title= Finiteness of central configurations of five bodies in the plane |journal=[[Annals of Mathematics]] |volume= 176 |year=2012 |pages=535–588 |doi=10.4007/annals.2012.176.1.10}}</ref>
|-
|style="text-align: center"| 7
| Distribution of points on the 2-sphere
| A noteworthy form of this problem is the [[Thomson Problem]] of equal point charges on a unit sphere governed by the electrostatic [[Coulomb's law]]. Very few exact N-point solutions are known while most solutions are numerical. Numerical solutions to this problem have been shown to correspond well with features of [[Electron configuration|electron shell-filling]] in [[Atomic structure]] found throughout the [[periodic table]].<ref>{{cite journal | first = T., Jr | last = LaFave |title= Correspondences between the classical electrostatic Thomson Problem and atomic electronic structure |url=http://www.pagesofmind.com/FullTextPubs/La13-LaFave-2013-Correspondences-between-the-Thomson-Problem-and-Atomic-Structure.pdf|accessdate= 11 Feb 2014| journal=Journal of Electrostatics |volume= 71 |issue=6 |year=2013 |pages=1029–1035|doi=10.1016/j.elstat.2013.10.001}}</ref> A well-defined, intermediate step to this problem involving a point charge at the origin has been reported.<ref>{{cite journal |first = T., Jr | last = LaFave |title= Discrete transformations in the Thomson Problem |url=http://www.pagesofmind.com/FullTextPubs/La14-LaFave-2014-Discrete-Transformations-in-the-Thomson-Problem.pdf|accessdate= 11 Feb 2014| journal=Journal of Electrostatics |volume= 72 |issue=1 |year=2014 |pages=39–43|doi=10.1016/j.elstat.2013.11.007}}</ref>
|-
|style="text-align: center"| 8
| Extend the mathematical model of [[general equilibrium theory]] to include [[price]] adjustments
|Gjerstad (2013) <ref>{{cite journal | first = Steven | last = Gjerstad |title= Price Dynamics in an Exchange Economy |url=http://link.springer.com/article/10.1007%2Fs00199-011-0651-5| journal=Economic Theory |volume= 52 |issue=2 |year=2013 |pages=461–500|doi=10.1007/s00199-011-0651-5}}</ref> extends the deterministic model of price adjustment to a stochastic model and shows that when the stochastic model is linearized around the equilibrium the result is the autoregressive price adjustment model used in applied econometrics. He then tests the model with price adjustment data from a general equilibrium experiment. The model performs well in a general equilibrium experiment with two commodities.
|-
|style="text-align: center"| 9
| The [[linear programming]] problem: find a [[Time complexity#Strongly and weakly polynomial time|strongly-polynomial time]] algorithm which for given matrix ''A'' ∈ '''R'''''m''×''n'' and ''b'' ∈ '''R'''''m'' decides whether there exists ''x'' ∈ '''R'''''n'' with ''Ax'' ≥ ''b''.
|
|-
|style="text-align: center"| 10
| [[Pugh's closing lemma]] (higher order of smoothness)
|
|-
|style="text-align: center"| 11
| Is one-dimensional dynamics generally hyperbolic?
| Smale states two variants of this problem: the complex-variable one ("Can a complex polynomial {{math|''T''}} be approximated by one of the same degree with the property that every critical point tends to a periodic sink under iteration?") and the real-variable version ("Can a smooth map {{math|''T'': [0,1] → [0,1]}} be {{math|''C''''r''}} approximated by one which is hyperbolic, for all {{math|''r'' > 1?}}"). The former remains open even in the simplest parameter space of polynomials, the [[Mandelbrot set]]. The latter was proved by Kozlovski, Shen and van Strien<ref>{{cite journal | first1 = O. | last1 = Kozlovski | first2 = W. | last2 = Shen | first3 = S. | last3 = van Strien |title= Density of hyperbolicity in dimension one|journal=[[Annals of Mathematics]] |volume= 166 |year=2007 |pages=145–182 |doi=10.4007/annals.2007.166.145}}</ref> in 2007.
|-bgcolor="99FF99"
|style="text-align: center"| 12
| [[Centralizer and normalizer|Centralizers]] of [[diffeomorphism]]s
| Solved in the C1 topology by C. Bonatti, S. Crovisier and [[Amie Wilkinson]]<ref>{{cite journal | first1 = C. | last1 = Bonatti | first2 = S. | last2 = Crovisier | first3 = A. | last3 = Wilkinson |title= The C1-generic diffeomorphism has trivial centralizer |journal=[[Publications Mathématiques de l'IHÉS]] |volume= 109 |year=2009 |pages=185–244 |doi=10.1007/s10240-009-0021-z}}</ref> in 2009.
|-
|style="text-align: center"| 13
| [[Hilbert's sixteenth problem|Hilbert's 16th problem]]
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 14
| [[Lorenz attractor]]
| Solved by [[Warwick Tucker]] in 2002 using [[interval arithmetic]].<ref>{{cite journal | first = Warwick | last = Tucker |title=A Rigorous ODE Solver and Smale's 14th Problem |journal=Foundations of Computational Mathematics |volume=2 |issue=1 |year=2002 |pages=53–117 |doi=10.1007/s002080010018 |url=http://www.math.cornell.edu/~warwick/main/rodes/JFoCM.pdf}}</ref>
|-
|style="text-align: center"| 15
| Do the [[Navier–Stokes equations]] in '''R'''3 always have a [[Navier–Stokes existence and smoothness|unique smooth solution]] that extends for all time?
|
|-
|style="text-align: center"| 16
| [[Jacobian conjecture]]
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 17
| Solving [[polynomial equations]] in [[P (complexity)|polynomial time]] in the average case
| C. Beltrán and L. M. Pardo found a uniform probabilistic algorithm (average [[Las Vegas algorithm]]) for Smale's 17th problem <ref>{{cite journal | first1 = Carlos | last1 = Beltrán | first2 = Luis Miguel | last2 = Pardo |title= On Smale's 17th Problem: A Probabilistic Positive answer |journal=Foundations of Computational Mathematics |volume=8 |issue=1 |year=2008 |pages=1–43 |doi=10.1007/s10208-005-0211-0 |url=http://personales.unican.es/beltranc/archivos/Smale17FoCM.pdf}}</ref><ref>{{cite journal | first1 = Carlos | last1 = Beltrán | first2 = Luis Miguel | last2 = Pardo |title= Smale's 17th Problem: Average Polynomial Time to compute affine and projective solutions|journal=Journal of the American Mathematical Society|volume=22 |year=2009 |pages=363–385|url=http://personales.unican.es/beltranc/archivos/AffSmale17JAMS.pdf |doi=10.1090/s0894-0347-08-00630-9}}</ref> F. Cucker and P. Bürgisser made the [[smoothed analysis]] of a probabilistic algorithm ''à la Beltrán-Pardo'', and then exhibited a deterministic algorithm running in time <math>N^{O(\log\log N)}</math>.<ref>{{cite journal | first1 = Felipe | last1 = Cucker | first2 = Peter | last2 = Bürgisser |title= On a problem posed by Steve Smale|journal=[[Annals of Mathematics]] |volume=174 |issue=3|year=2011 |doi=10.4007/annals.2011.174.3.8 |pages=1785–1836}} </ref>. Finally, P. Lairez found an alternative method to de--randomize the algorithm and thus found a deterministic algorithm which runs in average polynomial time<ref>{{cite journal | first1 = Pierre | last1 = Lairez |title= A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time |journal=Foundations of Computational Mathematics |volume=to appear |year=2016 }}</ref>. The problem is now considered as fully solved. All these works follow Shub and Smale's foundational work (the "Bezóut series") started in <ref>{{cite journal | first1 = Michael | last1 = Shub | first2 = Stephen | last2 = Smale |title= Complexity of Bézout's theorem. I. Geometric aspects |journal=J. Amer. Math. Soc. |volume=6 |issue=2 |year=1993 |pages=459-501 |doi=10.2307/2152805}}</ref>
|-
|style="text-align: center"| 18
| Limits of [[intelligence]] (It talks about the fundamental problems of intelligence and learning, both from the human and machine side)<ref>http://recursed.blogspot.jp/2006/02/tucson-day-3-interview-with-steve.html Friday, February 03, 2006 Tucson - Day 3 - Interview with Steve Smale </ref>
|
|}

Smale also listed three additional problems:<ref>{{cite journal | first = Steve | last = Smale|title = Mathematical Problems for the Next Century|journal = Mathematical Intelligencer|year =1998|volume=20|number=2|pages=7–15|id = {{citeseerx|10.1.1.35.4101}}|doi=10.1007/bf03025291}}</ref>
#[[Mean value problem]]
#Is the [[three-sphere]] a [[minimal set]]?
#Is an [[Anosov diffeomorphism]] of a [[compact manifold]] topologically the same as the [[Lie group]] model of John Franks?

== See also ==
* [[Millennium Prize Problems]]

== References ==
{{reflist|2}}

[[Category:Unsolved problems in mathematics]]

Smale's problems

2016-05-23T08:09:55Z

Beltranc:

'''Smale's problems''' are a list of eighteen [[unsolved problems in mathematics]] that was proposed by [[Stephen Smale|Steve Smale]] in 1998,<ref>{{cite journal | first = Steve | last = Smale|title = Mathematical Problems for the Next Century|journal = Mathematical Intelligencer|year =1998|volume=20|number=2|pages=7–15|id = {{citeseerx|10.1.1.35.4101}}|doi=10.1007/bf03025291}}</ref> republished in 1999.<ref>{{cite book | first = Steve | last = Smale |editor1-first = V. I. | editor1-last = Arnold | editor2-first = M. | editor2-last = Atiyah | editor3-first = P. | editor3-last = Lax | editor4-first = B. | editor4-last = Mazur | title=Mathematics: frontiers and perspectives |publisher=American Mathematical Society|year=1999|pages=271–294 |chapter=Mathematical problems for the next century|isbn=0821820702}}</ref> Smale composed this list in reply to a request from [[Vladimir Arnold]], then vice-president of the [[International Mathematical Union]], who asked several mathematicians to propose a list of problems for the 21st century. Arnold's inspiration came from the list of [[Hilbert's problems]] that had been published at the beginning of the 20th century.

== List of problems ==

{| class="wikitable"
! #
! width="40%"| Formulation !! Status
|-
|style="text-align: center"| 1
| [[Riemann hypothesis]] (see also [[Hilbert's eighth problem]])
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 2
| [[Poincaré conjecture]]
| Proved by [[Grigori Perelman]] in 2003 using [[Ricci flow]].<ref>{{cite arXiv | last = Perelman | first = Grigori | authorlink = Grigori Perelman | title = The entropy formula for the Ricci flow and its geometric applications | eprint = math.DG/0211159 | year = 2002 | class = math.DG }}</ref><ref>{{cite arXiv | last = Perelman | first = Grigori | title = Ricci flow with surgery on three-manifolds | eprint = math.DG/0303109 | year = 2003 | class = math.DG }}</ref><ref>{{cite arXiv | last = Perelman | first = Grigori | title = Finite extinction time for the solutions to the Ricci flow on certain three-manifolds | eprint = math.DG/0307245 | year = 2003 | class = math.DG }}</ref>
|-
|style="text-align: center"| 3
| [[P = NP problem|Does P = NP?]]
|
|-
|style="text-align: center"| 4
| Shub–Smale τ-conjecture on the integer zeros of a polynomial of one variable<ref>{{cite journal | last1=Shub | first1=Michael | last2=Smale | first2=Steve | title=On the intractability of Hilbert’s Nullstellensatz and an algebraic version of "NP≠P?" | zbl=0882.03040 | journal=Duke Math. J. | volume=81 | pages=47–54 | year=1995 | doi=10.1215/S0012-7094-95-08105-8 }}</ref><ref>{{cite book | last1=Bürgisser | first1=Peter | title=Completeness and reduction in algebraic complexity theory | zbl=0948.68082 | series=Algorithms and Computation in Mathematics | volume=7 | location=Berlin | publisher=[[Springer-Verlag]] | year=2000 | isbn=3-540-66752-0 | page=141 }}</ref>
|
|-
|style="text-align: center"| 5
| Height bounds for [[Diophantine equation|Diophantine curve]]s
|
|-
|style="text-align: center"| 6
| Finiteness of the number of relative equilibria in celestial mechanics
| Proved for five bodies by A. Albouy and V. Kaloshin in 2012.<ref>{{cite journal | first1 = A. | last1 = Albouy | first2 = V. | last2 = Kaloshin |title= Finiteness of central configurations of five bodies in the plane |journal=[[Annals of Mathematics]] |volume= 176 |year=2012 |pages=535–588 |doi=10.4007/annals.2012.176.1.10}}</ref>
|-
|style="text-align: center"| 7
| Distribution of points on the 2-sphere
| A noteworthy form of this problem is the [[Thomson Problem]] of equal point charges on a unit sphere governed by the electrostatic [[Coulomb's law]]. Very few exact N-point solutions are known while most solutions are numerical. Numerical solutions to this problem have been shown to correspond well with features of [[Electron configuration|electron shell-filling]] in [[Atomic structure]] found throughout the [[periodic table]].<ref>{{cite journal | first = T., Jr | last = LaFave |title= Correspondences between the classical electrostatic Thomson Problem and atomic electronic structure |url=http://www.pagesofmind.com/FullTextPubs/La13-LaFave-2013-Correspondences-between-the-Thomson-Problem-and-Atomic-Structure.pdf|accessdate= 11 Feb 2014| journal=Journal of Electrostatics |volume= 71 |issue=6 |year=2013 |pages=1029–1035|doi=10.1016/j.elstat.2013.10.001}}</ref> A well-defined, intermediate step to this problem involving a point charge at the origin has been reported.<ref>{{cite journal |first = T., Jr | last = LaFave |title= Discrete transformations in the Thomson Problem |url=http://www.pagesofmind.com/FullTextPubs/La14-LaFave-2014-Discrete-Transformations-in-the-Thomson-Problem.pdf|accessdate= 11 Feb 2014| journal=Journal of Electrostatics |volume= 72 |issue=1 |year=2014 |pages=39–43|doi=10.1016/j.elstat.2013.11.007}}</ref>
|-
|style="text-align: center"| 8
| Extend the mathematical model of [[general equilibrium theory]] to include [[price]] adjustments
|Gjerstad (2013) <ref>{{cite journal | first = Steven | last = Gjerstad |title= Price Dynamics in an Exchange Economy |url=http://link.springer.com/article/10.1007%2Fs00199-011-0651-5| journal=Economic Theory |volume= 52 |issue=2 |year=2013 |pages=461–500|doi=10.1007/s00199-011-0651-5}}</ref> extends the deterministic model of price adjustment to a stochastic model and shows that when the stochastic model is linearized around the equilibrium the result is the autoregressive price adjustment model used in applied econometrics. He then tests the model with price adjustment data from a general equilibrium experiment. The model performs well in a general equilibrium experiment with two commodities.
|-
|style="text-align: center"| 9
| The [[linear programming]] problem: find a [[Time complexity#Strongly and weakly polynomial time|strongly-polynomial time]] algorithm which for given matrix ''A'' ∈ '''R'''''m''×''n'' and ''b'' ∈ '''R'''''m'' decides whether there exists ''x'' ∈ '''R'''''n'' with ''Ax'' ≥ ''b''.
|
|-
|style="text-align: center"| 10
| [[Pugh's closing lemma]] (higher order of smoothness)
|
|-
|style="text-align: center"| 11
| Is one-dimensional dynamics generally hyperbolic?
| Smale states two variants of this problem: the complex-variable one ("Can a complex polynomial {{math|''T''}} be approximated by one of the same degree with the property that every critical point tends to a periodic sink under iteration?") and the real-variable version ("Can a smooth map {{math|''T'': [0,1] → [0,1]}} be {{math|''C''''r''}} approximated by one which is hyperbolic, for all {{math|''r'' > 1?}}"). The former remains open even in the simplest parameter space of polynomials, the [[Mandelbrot set]]. The latter was proved by Kozlovski, Shen and van Strien<ref>{{cite journal | first1 = O. | last1 = Kozlovski | first2 = W. | last2 = Shen | first3 = S. | last3 = van Strien |title= Density of hyperbolicity in dimension one|journal=[[Annals of Mathematics]] |volume= 166 |year=2007 |pages=145–182 |doi=10.4007/annals.2007.166.145}}</ref> in 2007.
|-bgcolor="99FF99"
|style="text-align: center"| 12
| [[Centralizer and normalizer|Centralizers]] of [[diffeomorphism]]s
| Solved in the C1 topology by C. Bonatti, S. Crovisier and [[Amie Wilkinson]]<ref>{{cite journal | first1 = C. | last1 = Bonatti | first2 = S. | last2 = Crovisier | first3 = A. | last3 = Wilkinson |title= The C1-generic diffeomorphism has trivial centralizer |journal=[[Publications Mathématiques de l'IHÉS]] |volume= 109 |year=2009 |pages=185–244 |doi=10.1007/s10240-009-0021-z}}</ref> in 2009.
|-
|style="text-align: center"| 13
| [[Hilbert's sixteenth problem|Hilbert's 16th problem]]
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 14
| [[Lorenz attractor]]
| Solved by [[Warwick Tucker]] in 2002 using [[interval arithmetic]].<ref>{{cite journal | first = Warwick | last = Tucker |title=A Rigorous ODE Solver and Smale's 14th Problem |journal=Foundations of Computational Mathematics |volume=2 |issue=1 |year=2002 |pages=53–117 |doi=10.1007/s002080010018 |url=http://www.math.cornell.edu/~warwick/main/rodes/JFoCM.pdf}}</ref>
|-
|style="text-align: center"| 15
| Do the [[Navier–Stokes equations]] in '''R'''3 always have a [[Navier–Stokes existence and smoothness|unique smooth solution]] that extends for all time?
|
|-
|style="text-align: center"| 16
| [[Jacobian conjecture]]
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 17
| Solving [[polynomial equations]] in [[P (complexity)|polynomial time]] in the average case
| C. Beltrán and L. M. Pardo found a uniform probabilistic algorithm (average [[Las Vegas algorithm]]) for Smale's 17th problem.<ref>{{cite journal | first1 = Carlos | last1 = Beltrán | first2 = Luis Miguel | last2 = Pardo |title= On Smale's 17th Problem: A Probabilistic Positive answer |journal=Foundations of Computational Mathematics |volume=8 |issue=1 |year=2008 |pages=1–43 |doi=10.1007/s10208-005-0211-0 |url=http://personales.unican.es/beltranc/archivos/Smale17FoCM.pdf}}</ref><ref>{{cite journal | first1 = Carlos | last1 = Beltrán | first2 = Luis Miguel | last2 = Pardo |title= Smale's 17th Problem: Average Polynomial Time to compute affine and projective solutions|journal=Journal of the American Mathematical Society|volume=22 |year=2009 |pages=363–385|url=http://personales.unican.es/beltranc/archivos/AffSmale17JAMS.pdf |doi=10.1090/s0894-0347-08-00630-9}}</ref> F. Cucker and P. Bürgisser made the [[smoothed analysis]] of a probabilistic algorithm ''à la Beltrán-Pardo'', and then exhibited a deterministic algorithm running in time <math>N^{O(\log\log N)}</math>.<ref>{{cite journal | first1 = Felipe | last1 = Cucker | first2 = Peter | last2 = Bürgisser |title= On a problem posed by Steve Smale|journal=[[Annals of Mathematics]] |volume=174 |issue=3|year=2011 |doi=10.4007/annals.2011.174.3.8 |pages=1785–1836}} </ref>. Finally, P. Lairez found an alternative method to de--randomize the algorithm and thus found a deterministic algorithm which runs in average polynomial time<ref>{{cite journal | first1 = Pierre | last1 = Lairez |title= A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time |journal=Foundations of Computational Mathematics |volume=to appear |year=2016 }}</ref>. The problem is now considered as fully solved.
|-
|style="text-align: center"| 18
| Limits of [[intelligence]] (It talks about the fundamental problems of intelligence and learning, both from the human and machine side)<ref>http://recursed.blogspot.jp/2006/02/tucson-day-3-interview-with-steve.html Friday, February 03, 2006 Tucson - Day 3 - Interview with Steve Smale </ref>
|
|}

Smale also listed three additional problems:<ref>{{cite journal | first = Steve | last = Smale|title = Mathematical Problems for the Next Century|journal = Mathematical Intelligencer|year =1998|volume=20|number=2|pages=7–15|id = {{citeseerx|10.1.1.35.4101}}|doi=10.1007/bf03025291}}</ref>
#[[Mean value problem]]
#Is the [[three-sphere]] a [[minimal set]]?
#Is an [[Anosov diffeomorphism]] of a [[compact manifold]] topologically the same as the [[Lie group]] model of John Franks?

== See also ==
* [[Millennium Prize Problems]]

== References ==
{{reflist|2}}

[[Category:Unsolved problems in mathematics]]

Smale's problems

2016-05-23T08:07:52Z

Beltranc: Included the recent breackthrough by Pierre Lairez in Smale's 17th problem

'''Smale's problems''' are a list of eighteen [[unsolved problems in mathematics]] that was proposed by [[Stephen Smale|Steve Smale]] in 1998,<ref>{{cite journal | first = Steve | last = Smale|title = Mathematical Problems for the Next Century|journal = Mathematical Intelligencer|year =1998|volume=20|number=2|pages=7–15|id = {{citeseerx|10.1.1.35.4101}}|doi=10.1007/bf03025291}}</ref> republished in 1999.<ref>{{cite book | first = Steve | last = Smale |editor1-first = V. I. | editor1-last = Arnold | editor2-first = M. | editor2-last = Atiyah | editor3-first = P. | editor3-last = Lax | editor4-first = B. | editor4-last = Mazur | title=Mathematics: frontiers and perspectives |publisher=American Mathematical Society|year=1999|pages=271–294 |chapter=Mathematical problems for the next century|isbn=0821820702}}</ref> Smale composed this list in reply to a request from [[Vladimir Arnold]], then vice-president of the [[International Mathematical Union]], who asked several mathematicians to propose a list of problems for the 21st century. Arnold's inspiration came from the list of [[Hilbert's problems]] that had been published at the beginning of the 20th century.

== List of problems ==

{| class="wikitable"
! #
! width="40%"| Formulation !! Status
|-
|style="text-align: center"| 1
| [[Riemann hypothesis]] (see also [[Hilbert's eighth problem]])
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 2
| [[Poincaré conjecture]]
| Proved by [[Grigori Perelman]] in 2003 using [[Ricci flow]].<ref>{{cite arXiv | last = Perelman | first = Grigori | authorlink = Grigori Perelman | title = The entropy formula for the Ricci flow and its geometric applications | eprint = math.DG/0211159 | year = 2002 | class = math.DG }}</ref><ref>{{cite arXiv | last = Perelman | first = Grigori | title = Ricci flow with surgery on three-manifolds | eprint = math.DG/0303109 | year = 2003 | class = math.DG }}</ref><ref>{{cite arXiv | last = Perelman | first = Grigori | title = Finite extinction time for the solutions to the Ricci flow on certain three-manifolds | eprint = math.DG/0307245 | year = 2003 | class = math.DG }}</ref>
|-
|style="text-align: center"| 3
| [[P = NP problem|Does P = NP?]]
|
|-
|style="text-align: center"| 4
| Shub–Smale τ-conjecture on the integer zeros of a polynomial of one variable<ref>{{cite journal | last1=Shub | first1=Michael | last2=Smale | first2=Steve | title=On the intractability of Hilbert’s Nullstellensatz and an algebraic version of "NP≠P?" | zbl=0882.03040 | journal=Duke Math. J. | volume=81 | pages=47–54 | year=1995 | doi=10.1215/S0012-7094-95-08105-8 }}</ref><ref>{{cite book | last1=Bürgisser | first1=Peter | title=Completeness and reduction in algebraic complexity theory | zbl=0948.68082 | series=Algorithms and Computation in Mathematics | volume=7 | location=Berlin | publisher=[[Springer-Verlag]] | year=2000 | isbn=3-540-66752-0 | page=141 }}</ref>
|
|-
|style="text-align: center"| 5
| Height bounds for [[Diophantine equation|Diophantine curve]]s
|
|-
|style="text-align: center"| 6
| Finiteness of the number of relative equilibria in celestial mechanics
| Proved for five bodies by A. Albouy and V. Kaloshin in 2012.<ref>{{cite journal | first1 = A. | last1 = Albouy | first2 = V. | last2 = Kaloshin |title= Finiteness of central configurations of five bodies in the plane |journal=[[Annals of Mathematics]] |volume= 176 |year=2012 |pages=535–588 |doi=10.4007/annals.2012.176.1.10}}</ref>
|-
|style="text-align: center"| 7
| Distribution of points on the 2-sphere
| A noteworthy form of this problem is the [[Thomson Problem]] of equal point charges on a unit sphere governed by the electrostatic [[Coulomb's law]]. Very few exact N-point solutions are known while most solutions are numerical. Numerical solutions to this problem have been shown to correspond well with features of [[Electron configuration|electron shell-filling]] in [[Atomic structure]] found throughout the [[periodic table]].<ref>{{cite journal | first = T., Jr | last = LaFave |title= Correspondences between the classical electrostatic Thomson Problem and atomic electronic structure |url=http://www.pagesofmind.com/FullTextPubs/La13-LaFave-2013-Correspondences-between-the-Thomson-Problem-and-Atomic-Structure.pdf|accessdate= 11 Feb 2014| journal=Journal of Electrostatics |volume= 71 |issue=6 |year=2013 |pages=1029–1035|doi=10.1016/j.elstat.2013.10.001}}</ref> A well-defined, intermediate step to this problem involving a point charge at the origin has been reported.<ref>{{cite journal |first = T., Jr | last = LaFave |title= Discrete transformations in the Thomson Problem |url=http://www.pagesofmind.com/FullTextPubs/La14-LaFave-2014-Discrete-Transformations-in-the-Thomson-Problem.pdf|accessdate= 11 Feb 2014| journal=Journal of Electrostatics |volume= 72 |issue=1 |year=2014 |pages=39–43|doi=10.1016/j.elstat.2013.11.007}}</ref>
|-
|style="text-align: center"| 8
| Extend the mathematical model of [[general equilibrium theory]] to include [[price]] adjustments
|Gjerstad (2013) <ref>{{cite journal | first = Steven | last = Gjerstad |title= Price Dynamics in an Exchange Economy |url=http://link.springer.com/article/10.1007%2Fs00199-011-0651-5| journal=Economic Theory |volume= 52 |issue=2 |year=2013 |pages=461–500|doi=10.1007/s00199-011-0651-5}}</ref> extends the deterministic model of price adjustment to a stochastic model and shows that when the stochastic model is linearized around the equilibrium the result is the autoregressive price adjustment model used in applied econometrics. He then tests the model with price adjustment data from a general equilibrium experiment. The model performs well in a general equilibrium experiment with two commodities.
|-
|style="text-align: center"| 9
| The [[linear programming]] problem: find a [[Time complexity#Strongly and weakly polynomial time|strongly-polynomial time]] algorithm which for given matrix ''A'' ∈ '''R'''''m''×''n'' and ''b'' ∈ '''R'''''m'' decides whether there exists ''x'' ∈ '''R'''''n'' with ''Ax'' ≥ ''b''.
|
|-
|style="text-align: center"| 10
| [[Pugh's closing lemma]] (higher order of smoothness)
|
|-
|style="text-align: center"| 11
| Is one-dimensional dynamics generally hyperbolic?
| Smale states two variants of this problem: the complex-variable one ("Can a complex polynomial {{math|''T''}} be approximated by one of the same degree with the property that every critical point tends to a periodic sink under iteration?") and the real-variable version ("Can a smooth map {{math|''T'': [0,1] → [0,1]}} be {{math|''C''''r''}} approximated by one which is hyperbolic, for all {{math|''r'' > 1?}}"). The former remains open even in the simplest parameter space of polynomials, the [[Mandelbrot set]]. The latter was proved by Kozlovski, Shen and van Strien<ref>{{cite journal | first1 = O. | last1 = Kozlovski | first2 = W. | last2 = Shen | first3 = S. | last3 = van Strien |title= Density of hyperbolicity in dimension one|journal=[[Annals of Mathematics]] |volume= 166 |year=2007 |pages=145–182 |doi=10.4007/annals.2007.166.145}}</ref> in 2007.
|-bgcolor="99FF99"
|style="text-align: center"| 12
| [[Centralizer and normalizer|Centralizers]] of [[diffeomorphism]]s
| Solved in the C1 topology by C. Bonatti, S. Crovisier and [[Amie Wilkinson]]<ref>{{cite journal | first1 = C. | last1 = Bonatti | first2 = S. | last2 = Crovisier | first3 = A. | last3 = Wilkinson |title= The C1-generic diffeomorphism has trivial centralizer |journal=[[Publications Mathématiques de l'IHÉS]] |volume= 109 |year=2009 |pages=185–244 |doi=10.1007/s10240-009-0021-z}}</ref> in 2009.
|-
|style="text-align: center"| 13
| [[Hilbert's sixteenth problem|Hilbert's 16th problem]]
|
|-
|-bgcolor="99FF99"
|style="text-align: center"| 14
| [[Lorenz attractor]]
| Solved by [[Warwick Tucker]] in 2002 using [[interval arithmetic]].<ref>{{cite journal | first = Warwick | last = Tucker |title=A Rigorous ODE Solver and Smale's 14th Problem |journal=Foundations of Computational Mathematics |volume=2 |issue=1 |year=2002 |pages=53–117 |doi=10.1007/s002080010018 |url=http://www.math.cornell.edu/~warwick/main/rodes/JFoCM.pdf}}</ref>
|-
|style="text-align: center"| 15
| Do the [[Navier–Stokes equations]] in '''R'''3 always have a [[Navier–Stokes existence and smoothness|unique smooth solution]] that extends for all time?
|
|-
|style="text-align: center"| 16
| [[Jacobian conjecture]]
|
|-
|style="text-align: center"| 17
| Solving [[polynomial equations]] in [[P (complexity)|polynomial time]] in the average case
| C. Beltrán and L. M. Pardo found a uniform probabilistic algorithm (average [[Las Vegas algorithm]]) for Smale's 17th problem.<ref>{{cite journal | first1 = Carlos | last1 = Beltrán | first2 = Luis Miguel | last2 = Pardo |title= On Smale's 17th Problem: A Probabilistic Positive answer |journal=Foundations of Computational Mathematics |volume=8 |issue=1 |year=2008 |pages=1–43 |doi=10.1007/s10208-005-0211-0 |url=http://personales.unican.es/beltranc/archivos/Smale17FoCM.pdf}}</ref><ref>{{cite journal | first1 = Carlos | last1 = Beltrán | first2 = Luis Miguel | last2 = Pardo |title= Smale's 17th Problem: Average Polynomial Time to compute affine and projective solutions|journal=Journal of the American Mathematical Society|volume=22 |year=2009 |pages=363–385|url=http://personales.unican.es/beltranc/archivos/AffSmale17JAMS.pdf |doi=10.1090/s0894-0347-08-00630-9}}</ref> F. Cucker and P. Bürgisser made the [[smoothed analysis]] of a probabilistic algorithm ''à la Beltrán-Pardo'', and then exhibited a deterministic algorithm running in time <math>N^{O(\log\log N)}</math>.<ref>{{cite journal | first1 = Felipe | last1 = Cucker | first2 = Peter | last2 = Bürgisser |title= On a problem posed by Steve Smale|journal=[[Annals of Mathematics]] |volume=174 |issue=3|year=2011 |doi=10.4007/annals.2011.174.3.8 |pages=1785–1836}} </ref>. Finally, P. Lairez found an alternative method to de--randomize the algorithm and thus found a deterministic algorithm which runs in average polynomial time<ref>{{cite journal | first1 = Pierre | last1 = Lairez |title= A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time |journal=Foundations of Computational Mathematics |volume=to appear |year=2016 }}</ref>
|-
|style="text-align: center"| 18
| Limits of [[intelligence]] (It talks about the fundamental problems of intelligence and learning, both from the human and machine side)<ref>http://recursed.blogspot.jp/2006/02/tucson-day-3-interview-with-steve.html Friday, February 03, 2006 Tucson - Day 3 - Interview with Steve Smale </ref>
|
|}

Smale also listed three additional problems:<ref>{{cite journal | first = Steve | last = Smale|title = Mathematical Problems for the Next Century|journal = Mathematical Intelligencer|year =1998|volume=20|number=2|pages=7–15|id = {{citeseerx|10.1.1.35.4101}}|doi=10.1007/bf03025291}}</ref>
#[[Mean value problem]]
#Is the [[three-sphere]] a [[minimal set]]?
#Is an [[Anosov diffeomorphism]] of a [[compact manifold]] topologically the same as the [[Lie group]] model of John Franks?

== See also ==
* [[Millennium Prize Problems]]

== References ==
{{reflist|2}}

[[Category:Unsolved problems in mathematics]]

Wolfgang Dahmen

2015-07-28T13:21:13Z

Beltranc:

[[File:Wolfgang Dahmen.jpg|thumb|Wolfgang Dahmen.]]
'''Wolfgang Dahmen''' (born 1949) is a German [[mathematician]] working in [[approximation theory]], [[numerical analysis]], and [[partial differential equations]]. In 2002 he was awarded the [[Gottfried Wilhelm Leibniz Prize]]. He was also a [[taekwondo]] athlete. He has been the Chair of the [[Foundations of Computational Mathematics | Society for the Foundations of Computational Mathematics]] (2014-).

==References==
*[http://books.google.co.uk/books?id=qHB518aP9r0C Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang Dahmen on the Occasion of His 60th Birthday], Ronald DeVore, Angela Kunoth, Springer, 2009, ISBN 978-3-642-03412-1
*[http://www.igpm.rwth-aachen.de/node/184 Homepage at Institut für Geometrie und Praktische Mathematik]

{{Authority control}}
{{Persondata 
| NAME = Dahmen, Wolfgang
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = German taekwondo practitioner and mathematician
| DATE OF BIRTH = 1949
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Dahmen, Wolfgang}}
[[Category:20th-century German mathematicians]]
[[Category:21st-century German mathematicians]]
[[Category:Living people]]
[[Category:German taekwondo practitioners]]
[[Category:1949 births]]

{{Germany-mathematician-stub}}

Endre Süli

2015-07-28T13:20:44Z

Beltranc:

{{Infobox scientist
|name = Endre Süli
|image = Endre Süli.jpg
|caption = Oberwolfach, 2007
|birth_date = {{birth date and age|df=yes|1956|06|21}}
|birth_place = [[Yugoslavia]]
|death_date =
|death_place =
|residence = {{flag|United Kingdom}}
|citizenship = [[United Kingdom|British]] and [[Serbia]]n
|nationality = [[Hungarian people|Hungarian]]
|ethnicity =
|field = [[Numerical analysis]] of [[partial differential equations]]
|work_institutions = [[University of Belgrade]] 1978-1985 [[University of Oxford]] 1985-
|alma_mater = [[University of Belgrade]] B.Sc. 1978, M.Sc. 1980, Ph.D. 1985 [[University of Oxford]] MA 1985
|doctoral_advisor =
|known_for =
|author_abbrev_bot =
|author_abbrev_zoo =
|awards =
|influences =
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|prizes =
|religion =
|footnotes =
|signature =
}}

'''Endre Süli''' (also, Endre Suli) is Professor of [[Numerical Analysis]] in the [[The Mathematical Institute, University of Oxford|Mathematical Institute]], [[University of Oxford]], [[Fellow]] and [[Tutor]] in Mathematics at [[Worcester College, Oxford]] and [[Supernumerary]] Fellow of [[Linacre College, Oxford]]. He was educated at the [[University of Belgrade]] and, as a [[British Council]] Visiting Student, at the [[University of Reading]] and [[St Catherine's College, Oxford]].
His research is concerned with the mathematical analysis of numerical algorithms for nonlinear partial differential equations.

Süli is Foreign Member of the [[Serbian Academy of Sciences and Arts]] (2009) and Fellow of the [[European Academy of Sciences]] (2010). He was invited speaker at the [[International Congress of Mathematicians]] in Madrid in 2006<ref name="icm2006">{{cite web|url=http://icm2006.org/v_f/fr_Resultat.php?CodiTipusEvent=2il&Botons=datr&Ordenacio=cr&PagIni=2il&PagIni=2il&Titol=Invited%20lectures.%2016.%20Numerical%20Analysis%20and%20Scientific%20Computing&CodiSeccio=16&CodiSeccioNo=--/|title=International Congress of Mathematicians, Madrid, 2006}}</ref> and was Chair of the [[Foundations of Computational Mathematics | Society for the Foundations of Computational Mathematics]]
(2002–2005).<ref name="focm">{{cite web|url=http://www.focm.net/|title=Foundations of Computational Mathematics}}</ref> Other honours include: Fellow of the Institute of Mathematics and its Applications ([[FIMA]], 2007-), Charlemagne Distinguished Lecture (2011), IMA Service Award (2011), Professor Hospitus Universitatis Carolinae Pragensis, [[Charles University in Prague]] (2012–), Distinguished Visiting Chair Professor [[Shanghai Jiao Tong University]] (2013–), President, SIAM United Kingdom and Republic of Ireland Section (2013–2015), [[London Mathematical Society]]/[[New Zealand Mathematical Society]] Forder Lecturer (2015),<ref name="forder">{{cite web|url=http://www.lms.ac.uk/events/lectures/forder-and-aitken-lectureship|title=LMS-NZMS Forder Lectureship}}</ref> Aziz Lecture (2015). Since 2005 Süli has been co-Editor-in-Chief of the IMA Journal of Numerical Analysis<ref name="imajna">{{cite web|url=http://imajna.oxfordjournals.org/|title=IMA Journal of Numerical Analysis}}</ref> and is a [http://global.oup.com/about/structure?cc=gb Delegate] of [[Oxford University Press]]. He is a member of the Scientific Committee of the Mathematisches Forschungsinstitut Oberwolfach ([[Mathematical Research Institute of Oberwolfach]]),
the Scientific Council of [[Société de Mathématiques Appliquées et Industrielles]] (SMAI), and was a member of the Scientific Steering Committee of the [[Isaac Newton Institute for Mathematical Sciences]] at the [[University of Cambridge]] (2011–2014), and the Scientific Advisory Board of the Archimedes Center for Modeling, Analysis and Computation at the University of Crete.<ref name="acmac">{{cite web|url=http://www.acmac.uoc.gr/|title=Archimedes Center for Modeling, Analysis and Computation}}</ref>

==Notes==
<references />

==External links==
*[https://www.maths.ox.ac.uk/people/endre.suli Endre Süli's official home page at the University of Oxford]
*{{MathGenealogy |id=53896}}

{{Authority control}}

{{Persondata 
| NAME = Suli, Endre
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = British mathematician
| DATE OF BIRTH = 21 June 1956
| PLACE OF BIRTH = [[Serbia]], former [[Yugoslavia]]
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Suli, Endre}}
[[Category:Numerical analysts]]
[[Category:People associated with the finite element method]]
[[Category:Hungarian mathematicians]]
[[Category:Yugoslav emigrants to the United Kingdom]]
[[Category:Serbian mathematicians]]
[[Category:Members of the Serbian Academy of Sciences and Arts]]
[[Category:20th-century British mathematicians]]
[[Category:21st-century British mathematicians]]
[[Category:Oxford University Press Delegate]]
[[Category:Fellows of Worcester College, Oxford]]
[[Category:Fellows of Linacre College, Oxford]]
[[Category:Alumni of St Catherine's College, Oxford]]
[[Category:University of Belgrade Faculty of Mathematics alumni]]
[[Category:1956 births]]
[[Category:Living people]]

{{Serbian-academic-bio-stub}}
{{UK-mathematician-stub}}

Ronald DeVore

2015-07-28T13:20:19Z

Beltranc: /* Awards and honors */

{{Infobox scientist
| boxwidth =
| name = Ronald A. DeVore
| image = Ronald DeVore.jpg
| image_size =
| alt =
| caption =
| birth_date = May 14, 1941
| birth_place = [[Detroit]], [[Michigan]]
| residence =
| nationality = {{flagicon|US}} [[US|American]]
| fields = [[Mathematician]]
| workplaces = [[Texas A&M University]]
| alma_mater = [[Ohio State University]] [[Eastern Michigan University]]
| doctoral_advisor = Ranko Bojanic
| academic_advisors =
| doctoral_students =
| notable_students =
| known_for = [[Approximation theory]], [[Wavelet| Wavelet theory]], [[Compressed sensing|Compressive sensing]]
| awards = Member of [[Bulgarian Academy of Sciences]] (2007) 
[[SPIE]] Wavelet Pioneer Award (2007) 
Plenary Lecturer, [[International Congress of Mathematicians]] (2006) 
Honorary Doctorate, [[RWTH Aachen University]] (2004) 
[[Humboldt Prize]] (2002) 
Member of [[American Academy of Arts and Sciences]] (2001) 
Bulgarian Gold Medal of Science (2001) 
Journal of Complexity Outstanding Paper Award (2000)
}}

'''Ronald Alvin DeVore''' (born May 14, 1941) is the Walter E. Koss Professor of [[Mathematics]] at [[Texas A&M University]].

==Academic biography==
DeVore received a B.S. from [[Eastern Michigan University]] in 1964 and a Ph.D. in [[mathematics]] from [[Ohio State University]] in 1967 under the supervision of Ranko Bojanic.<ref name="mg">{{mathgenealogy|name=Ronald Alvin DeVore|id=10109}}.</ref> From 1968 to 1977 he was at [[Oakland University]]. In 1977 he became a professor at the [[University of South Carolina]], where he served as the Robert L. Sumwalt Professor of Mathematics from 1986 to 2005. From 1999 to 2005 he also served as the director of the Industrial Mathematics Institutes, which he founded. In 2005 he retired from the [[University of South Carolina]]. Since 2008 he has been the Walter E. Koss Professor at [[Texas A&M University]] and will be named Distinguished Professor in Fall 2010.<ref name="current_cv">[http://www.math.tamu.edu/~rdevore/currentvitae.html Ronald A. DeVore Current Vitae]</ref>

DeVore has been a visiting professor at a number of universities around the world, including: [[Ohio State University]] (1967–1968), the [[University of Alberta]] (1971–1972), [[Universitat Erlangen-Nurnberg]] (1975–1976), [[Universitat Bonn]] (1977, 1978, 1979), [[Texas A&M University]] (1983), [[Scuola Normale di Pisa]] (1984), the [[University of Wisconsin]] (1983–1984, 1985, 1991), [[Purdue University]] (1990), the [[University of Paris VI]] (1996, 2000, 2002, 2004, 2005), [[Princeton University]] (1997–1998), [[RWTH Aachen University]] (2002), the [[University of Maryland]] (2004–2005), [[Rice University]] (2005–2006), the [[Courant Institute]] at [[New York University]] (2006–2007), and the Fondation Sciences Mathématiques de Paris (2009–2010).<ref name="current_cv" />

==Research==
DeVore has been active in the development of many areas of applied mathematics such as [[numerical analysis]] of [[partial differential equations]], [[machine learning]] algorithms, [[approximation theory|approximation]] of functions, [[wavelets|wavelet transforms]], and [[statistics]]. He has also made significant contributions to the theory of [[compressed sensing|compressive sensing]].

==Awards and honors==
DeVore has received numerous awards, including an [[Alexander von Humboldt]] Fellowship from 1975 to 1976, the Journal of Complexity Outstanding Paper Award in 2000, the Bulgarian Gold Medal of Science in 2001, the [[Humboldt Prize]] in 2002, the
ICS Hot Paper Award in 2003, an honorary doctorate from [[RWTH Aachen University]] in 2004,<ref>[http://www.igpm.rwth-aachen.de/www/Awards/award.html Honorary doctorate award for Prof. Ronald DeVore, Ph.D.], 2004.</ref> and the [[SPIE]] Wavelet Pioneer Award in 2007. He was also a plenary lecturer at the [[International Congress of Mathematicians]] in 2006.<ref>[http://icm2006.org/v_f/web_fr.php?PagIni=1pl Plenary Lectures], ICM, 2006.</ref>

In 2001 he became a member of the [[American Academy of Arts and Sciences]],<ref>[http://www.amacad.org/pdfs/alphaList09.pdf Alphabetical Index of Active Members], [[American Academy of Arts and Sciences]], 2009.</ref> and in 2007 he became a member of the [[Bulgarian Academy of Sciences]]. In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10.</ref>. From 2000 to 2002 he was the Chair of the [[Foundations of Computational Mathematics | Society for the Foundations of Computational Mathematics]]

==References==
{{reflist}}

==External links==
*[http://www.math.tamu.edu/~rdevore/ DeVore's web page] at Texas A&M.

{{Authority control}}

{{Persondata 
| NAME = Devore, Ronald A.
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = May 14, 1941
| PLACE OF BIRTH = [[Detroit]], [[Michigan]]
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Devore, Ronald A.}}
[[Category:Living people]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Texas A&M University faculty]]
[[Category:Ohio State University alumni]]
[[Category:Purdue University faculty]]
[[Category:Rice University staff]]
[[Category:1941 births]]
[[Category:Eastern Michigan University alumni]]
[[Category:University of South Carolina faculty]]
[[Category:Oakland University faculty]]
[[Category:Fellows of the American Mathematical Society]]

Arieh Iserles

2015-07-28T13:19:58Z

Beltranc:

{{Use dmy dates|date=December 2012}}
{{Use British English|date=December 2012}}
{{Infobox scientist
|name = Arieh Iserles
|image =
|birth_date = {{birth date and age|1947|09|02|df=y}}
|birth_place =
|death_date =
|death_place =
|residence = [[Cambridge, England]]
|citizenship =
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|ethnicity =
|field =
|work_institutions = [[University of Cambridge]]
|alma_mater = [[Hebrew University of Jerusalem]], [[Ben-Gurion University of the Negev]]
|doctoral_advisor =
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|known_for =
|author_abbrev_bot =
|author_abbrev_zoo =
|influences =
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|footnotes =
|signature =
}}

'''Arieh Iserles''' (born 2 September 1947) is a [[computational mathematics|computational mathematician]], currently Professor of the Numerical Analysis of Differential Equations at the [[University of Cambridge]] and a member of the [[Faculty of Mathematics, University of Cambridge|Department of Applied Mathematics and Theoretical Physics]].

He studied at the [[Hebrew University of Jerusalem]] and [[Ben-Gurion University of the Negev]] and wrote his PhD dissertation on numerical methods for stiff ordinary differential equations. His research comprises many themes in computational and applied mathematics: ordinary and partial differential equations, approximation theory, geometric numerical integration, orthogonal polynomials, functional equations, computational dynamics and the computation of highly oscillatory phenomena.

He has written a textbook, ''A First Course in the Numerical Analysis of Differential Equations'' (Cambridge University Press, 2nd ed. 2009).<ref>http://www.cambridge.org/gb/knowledge/isbn/item2327165/?site_locale=en_GB</ref>

Arieh Iserles is the Managing Editor of [[Acta Numerica]], Editor-in-Chief of IMA Journal of Numerical Analysis<ref>http://imajna.oxfordjournals.org/</ref> and an editor of several other mathematical journals. From 1997 to 2000 he was the chair of the [[Foundations of Computational Mathematics | Society for the Foundations of Computational Mathematics]].<ref>http://www.focm.net</ref>

He is currently a Director of the [http://www.maths.cam.ac.uk/postgrad/cca/ Cambridge Centre for Analysis (CCA)], an [[EPSRC]]-funded [[Doctoral Training Centre|Centre for Doctoral Training]] in [[mathematical analysis]].

In 1999, he was awarded the Onsager Medal, by the [[Norwegian University of Science and Technology]], in 2012 he received the [[David Crighton]] medal,<ref>http://www.ima.org.uk/about_us/awards_and_medals/david_crighton_medal.cfm</ref> presented by the [[Institute of Mathematics and its Applications]] and [[London Mathematical Society]] "for services to mathematics and the mathematics community"<ref>http://www.ima.org.uk/viewitem.cfm?cit_id=384309</ref> and in 2014 he was awarded by [[Society for Industrial and Applied Mathematics]] the SIAM Prize for Distinguished Service to the Profession.<ref>http://www.siam.org/prizes/sponsored/dist_service.php</ref> In 2012, Professor Iserles was an invited speaker at the 6th European Congress of Mathematics <ref>http://www.6ecm.pl/en</ref> in Kraków, 2–7 July 2012.

== External links ==
* [http://www.damtp.cam.ac.uk/user/na/people/Arieh/ Professor Iserles' website]

== References ==

{{Reflist}}

{{Persondata 
| NAME =Iserles, Arieh
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = British mathematician
| DATE OF BIRTH =2 September 1947
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Iserles, Arieh}}
[[Category:1947 births]]
[[Category:Living people]]
[[Category:Ben-Gurion University of the Negev alumni]]
[[Category:Hebrew University of Jerusalem alumni]]
[[Category:Mathematical analysts]]
[[Category:Members of the Department of Applied Mathematics and Theoretical Physics]]

{{UK-mathematician-stub}}

Michael Shub

2015-07-28T13:19:37Z

Beltranc: /* Work */

{{Infobox person
| name = Michael Shub
| image = Michael Shub.jpg
| alt =
| caption = Michael Shub in April 2012
| birth_name = Michael Ira Shub
| birth_date = {{Birth date and age|1943|08|17}}
| birth_place =
| death_date = 
| death_place =
| nationality = USA
| other_names =
| occupation = mathematician, professor
| known_for = [[Blum Blum Shub]] [[pseudorandom number generator]]
| alma_mater = [[University of California, Berkeley]]
}}
'''Michael Ira Shub''' (born August 17, 1943) is an [[United States|American]] [[mathematician]] who has done research into [[Dynamical Systems]] and the Complexity of Real Number Algorithms.

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkeley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

Shub was the Chair of the [[Foundations of Computational Mathematics | Society for the Foundations of Computational Mathematics]] from 1995 to 1997. In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>

== Work ==

Shub has produced publications in dynamical systems and in the complexity of real number algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps, which gave the first examples of structurally stable strange attractors. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems.<ref>Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref><ref>Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref><ref>Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator. see [[Blum Blum Shub]]. This is said to be useful from theoretical and practical perspectives. See.<ref>Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005</ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model is used to analyse the computability of functions.<ref>Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigorous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref>Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association [[Foundations of Computational Mathematics]], and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|author2=Blum, Manuel |author3=Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27–41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.<ref>{{cite journal|author=Robbin, Joel|title=Review: ''Global stability of dynamical systems'' by Michael Shub|journal=Bull. Amer. Math. Soc. (N.S.)|year=1988|volume=18|issue=2|pages=248–250|url=http://www.ams.org/journals/bull/1988-18-02/S0273-0979-1988-15665-0/S0273-0979-1988-15665-0.pdf|doi=10.1090/s0273-0979-1988-15665-0}}</ref>

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, July 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale [https://books.google.com/books/about/Complexity_and_Real_Computation.html?id=zxtrVqUP-AwC ''Complexity and Real Computation''] Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

{{Authority control|3=282048 |2=n85 |1=LCCN}}
{{Persondata
| NAME = Michael Ira Shub
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = August 17, 1943
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Shub, Michael Ira}}
[[Category:1943 births]]
[[Category:Living people]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:University of California, Berkeley alumni]]

Michael Shub

2015-07-28T13:19:04Z

Beltranc: /* Biography */

{{Infobox person
| name = Michael Shub
| image = Michael Shub.jpg
| alt =
| caption = Michael Shub in April 2012
| birth_name = Michael Ira Shub
| birth_date = {{Birth date and age|1943|08|17}}
| birth_place =
| death_date = 
| death_place =
| nationality = USA
| other_names =
| occupation = mathematician, professor
| known_for = [[Blum Blum Shub]] [[pseudorandom number generator]]
| alma_mater = [[University of California, Berkeley]]
}}
'''Michael Ira Shub''' (born August 17, 1943) is an [[United States|American]] [[mathematician]] who has done research into [[Dynamical Systems]] and the Complexity of Real Number Algorithms.

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkeley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

Shub was the Chair of the [[Foundations of Computational Mathematics | Society for the Foundations of Computational Mathematics]] from 1995 to 1997. In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>

== Work ==

Shub has produced publications in dynamical systems and in the complexity of real number algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps, which gave the first examples of structurally stable strange attractors. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems.<ref>Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref><ref>Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref><ref>Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator. see [[Blum Blum Shub]]. This is said to be useful from theoretical and practical perspectives. See.<ref>Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005</ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model is used to analyse the computability of functions.<ref>Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigorous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref>Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|author2=Blum, Manuel |author3=Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27–41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.<ref>{{cite journal|author=Robbin, Joel|title=Review: ''Global stability of dynamical systems'' by Michael Shub|journal=Bull. Amer. Math. Soc. (N.S.)|year=1988|volume=18|issue=2|pages=248–250|url=http://www.ams.org/journals/bull/1988-18-02/S0273-0979-1988-15665-0/S0273-0979-1988-15665-0.pdf|doi=10.1090/s0273-0979-1988-15665-0}}</ref>

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, July 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale [https://books.google.com/books/about/Complexity_and_Real_Computation.html?id=zxtrVqUP-AwC ''Complexity and Real Computation''] Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

{{Authority control|3=282048 |2=n85 |1=LCCN}}
{{Persondata
| NAME = Michael Ira Shub
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = August 17, 1943
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Shub, Michael Ira}}
[[Category:1943 births]]
[[Category:Living people]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:University of California, Berkeley alumni]]

Wolfgang Dahmen

2015-07-28T12:47:41Z

Beltranc:

[[File:Wolfgang Dahmen.jpg|thumb|Wolfgang Dahmen.]]
'''Wolfgang Dahmen''' (born 1949) is a German [[mathematician]] working in [[approximation theory]], [[numerical analysis]], and [[partial differential equations]]. In 2002 he was awarded the [[Gottfried Wilhelm Leibniz Prize]]. He was also a [[taekwondo]] athlete. He has been the Chair of the society for [[Foundations of Computational Mathematics]] (2014-).

==References==
*[http://books.google.co.uk/books?id=qHB518aP9r0C Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang Dahmen on the Occasion of His 60th Birthday], Ronald DeVore, Angela Kunoth, Springer, 2009, ISBN 978-3-642-03412-1
*[http://www.igpm.rwth-aachen.de/node/184 Homepage at Institut für Geometrie und Praktische Mathematik]

{{Authority control}}
{{Persondata 
| NAME = Dahmen, Wolfgang
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = German taekwondo practitioner and mathematician
| DATE OF BIRTH = 1949
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Dahmen, Wolfgang}}
[[Category:20th-century German mathematicians]]
[[Category:21st-century German mathematicians]]
[[Category:Living people]]
[[Category:German taekwondo practitioners]]
[[Category:1949 births]]

{{Germany-mathematician-stub}}

Endre Süli

2015-07-28T12:46:49Z

Beltranc:

{{Infobox scientist
|name = Endre Süli
|image = Endre Süli.jpg
|caption = Oberwolfach, 2007
|birth_date = {{birth date and age|df=yes|1956|06|21}}
|birth_place = [[Yugoslavia]]
|death_date =
|death_place =
|residence = {{flag|United Kingdom}}
|citizenship = [[United Kingdom|British]] and [[Serbia]]n
|nationality = [[Hungarian people|Hungarian]]
|ethnicity =
|field = [[Numerical analysis]] of [[partial differential equations]]
|work_institutions = [[University of Belgrade]] 1978-1985 [[University of Oxford]] 1985-
|alma_mater = [[University of Belgrade]] B.Sc. 1978, M.Sc. 1980, Ph.D. 1985 [[University of Oxford]] MA 1985
|doctoral_advisor =
|known_for =
|author_abbrev_bot =
|author_abbrev_zoo =
|awards =
|influences =
|influenced =
|prizes =
|religion =
|footnotes =
|signature =
}}

'''Endre Süli''' (also, Endre Suli) is Professor of [[Numerical Analysis]] in the [[The Mathematical Institute, University of Oxford|Mathematical Institute]], [[University of Oxford]], [[Fellow]] and [[Tutor]] in Mathematics at [[Worcester College, Oxford]] and [[Supernumerary]] Fellow of [[Linacre College, Oxford]]. He was educated at the [[University of Belgrade]] and, as a [[British Council]] Visiting Student, at the [[University of Reading]] and [[St Catherine's College, Oxford]].
His research is concerned with the mathematical analysis of numerical algorithms for nonlinear partial differential equations.

Süli is Foreign Member of the [[Serbian Academy of Sciences and Arts]] (2009) and Fellow of the [[European Academy of Sciences]] (2010). He was invited speaker at the [[International Congress of Mathematicians]] in Madrid in 2006<ref name="icm2006">{{cite web|url=http://icm2006.org/v_f/fr_Resultat.php?CodiTipusEvent=2il&Botons=datr&Ordenacio=cr&PagIni=2il&PagIni=2il&Titol=Invited%20lectures.%2016.%20Numerical%20Analysis%20and%20Scientific%20Computing&CodiSeccio=16&CodiSeccioNo=--/|title=International Congress of Mathematicians, Madrid, 2006}}</ref> and was Chair of the society [[Foundations of Computational Mathematics]]
(2002–2005).<ref name="focm">{{cite web|url=http://www.focm.net/|title=Foundations of Computational Mathematics}}</ref> Other honours include: Fellow of the Institute of Mathematics and its Applications ([[FIMA]], 2007-), Charlemagne Distinguished Lecture (2011), IMA Service Award (2011), Professor Hospitus Universitatis Carolinae Pragensis, [[Charles University in Prague]] (2012–), Distinguished Visiting Chair Professor [[Shanghai Jiao Tong University]] (2013–), President, SIAM United Kingdom and Republic of Ireland Section (2013–2015), [[London Mathematical Society]]/[[New Zealand Mathematical Society]] Forder Lecturer (2015),<ref name="forder">{{cite web|url=http://www.lms.ac.uk/events/lectures/forder-and-aitken-lectureship|title=LMS-NZMS Forder Lectureship}}</ref> Aziz Lecture (2015). Since 2005 Süli has been co-Editor-in-Chief of the IMA Journal of Numerical Analysis<ref name="imajna">{{cite web|url=http://imajna.oxfordjournals.org/|title=IMA Journal of Numerical Analysis}}</ref> and is a [http://global.oup.com/about/structure?cc=gb Delegate] of [[Oxford University Press]]. He is a member of the Scientific Committee of the Mathematisches Forschungsinstitut Oberwolfach ([[Mathematical Research Institute of Oberwolfach]]),
the Scientific Council of [[Société de Mathématiques Appliquées et Industrielles]] (SMAI), and was a member of the Scientific Steering Committee of the [[Isaac Newton Institute for Mathematical Sciences]] at the [[University of Cambridge]] (2011–2014), and the Scientific Advisory Board of the Archimedes Center for Modeling, Analysis and Computation at the University of Crete.<ref name="acmac">{{cite web|url=http://www.acmac.uoc.gr/|title=Archimedes Center for Modeling, Analysis and Computation}}</ref>

==Notes==
<references />

==External links==
*[https://www.maths.ox.ac.uk/people/endre.suli Endre Süli's official home page at the University of Oxford]
*{{MathGenealogy |id=53896}}

{{Authority control}}

{{Persondata 
| NAME = Suli, Endre
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = British mathematician
| DATE OF BIRTH = 21 June 1956
| PLACE OF BIRTH = [[Serbia]], former [[Yugoslavia]]
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Suli, Endre}}
[[Category:Numerical analysts]]
[[Category:People associated with the finite element method]]
[[Category:Hungarian mathematicians]]
[[Category:Yugoslav emigrants to the United Kingdom]]
[[Category:Serbian mathematicians]]
[[Category:Members of the Serbian Academy of Sciences and Arts]]
[[Category:20th-century British mathematicians]]
[[Category:21st-century British mathematicians]]
[[Category:Oxford University Press Delegate]]
[[Category:Fellows of Worcester College, Oxford]]
[[Category:Fellows of Linacre College, Oxford]]
[[Category:Alumni of St Catherine's College, Oxford]]
[[Category:University of Belgrade Faculty of Mathematics alumni]]
[[Category:1956 births]]
[[Category:Living people]]

{{Serbian-academic-bio-stub}}
{{UK-mathematician-stub}}

Michael Shub

2015-07-28T12:46:07Z

Beltranc: /* Biography */

{{Infobox person
| name = Michael Shub
| image = Michael Shub.jpg
| alt =
| caption = Michael Shub in April 2012
| birth_name = Michael Ira Shub
| birth_date = {{Birth date and age|1943|08|17}}
| birth_place =
| death_date = 
| death_place =
| nationality = USA
| other_names =
| occupation = mathematician, professor
| known_for = [[Blum Blum Shub]] [[pseudorandom number generator]]
| alma_mater = [[University of California, Berkeley]]
}}
'''Michael Ira Shub''' (born August 17, 1943) is an [[United States|American]] [[mathematician]] who has done research into [[Dynamical Systems]] and the Complexity of Real Number Algorithms.

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkeley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

Shub was the Chair of the society [[Foundations of Computational Mathematics]] from 1995 to 1997. In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>

== Work ==

Shub has produced publications in dynamical systems and in the complexity of real number algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps, which gave the first examples of structurally stable strange attractors. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems.<ref>Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref><ref>Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref><ref>Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator. see [[Blum Blum Shub]]. This is said to be useful from theoretical and practical perspectives. See.<ref>Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005</ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model is used to analyse the computability of functions.<ref>Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigorous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref>Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|author2=Blum, Manuel |author3=Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27–41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.<ref>{{cite journal|author=Robbin, Joel|title=Review: ''Global stability of dynamical systems'' by Michael Shub|journal=Bull. Amer. Math. Soc. (N.S.)|year=1988|volume=18|issue=2|pages=248–250|url=http://www.ams.org/journals/bull/1988-18-02/S0273-0979-1988-15665-0/S0273-0979-1988-15665-0.pdf|doi=10.1090/s0273-0979-1988-15665-0}}</ref>

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, July 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale [https://books.google.com/books/about/Complexity_and_Real_Computation.html?id=zxtrVqUP-AwC ''Complexity and Real Computation''] Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

{{Authority control|3=282048 |2=n85 |1=LCCN}}
{{Persondata
| NAME = Michael Ira Shub
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = August 17, 1943
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Shub, Michael Ira}}
[[Category:1943 births]]
[[Category:Living people]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:University of California, Berkeley alumni]]

Ronald DeVore

2015-07-28T12:45:38Z

Beltranc: /* Awards and honors */

{{Infobox scientist
| boxwidth =
| name = Ronald A. DeVore
| image = Ronald DeVore.jpg
| image_size =
| alt =
| caption =
| birth_date = May 14, 1941
| birth_place = [[Detroit]], [[Michigan]]
| residence =
| nationality = {{flagicon|US}} [[US|American]]
| fields = [[Mathematician]]
| workplaces = [[Texas A&M University]]
| alma_mater = [[Ohio State University]] [[Eastern Michigan University]]
| doctoral_advisor = Ranko Bojanic
| academic_advisors =
| doctoral_students =
| notable_students =
| known_for = [[Approximation theory]], [[Wavelet| Wavelet theory]], [[Compressed sensing|Compressive sensing]]
| awards = Member of [[Bulgarian Academy of Sciences]] (2007) 
[[SPIE]] Wavelet Pioneer Award (2007) 
Plenary Lecturer, [[International Congress of Mathematicians]] (2006) 
Honorary Doctorate, [[RWTH Aachen University]] (2004) 
[[Humboldt Prize]] (2002) 
Member of [[American Academy of Arts and Sciences]] (2001) 
Bulgarian Gold Medal of Science (2001) 
Journal of Complexity Outstanding Paper Award (2000)
}}

'''Ronald Alvin DeVore''' (born May 14, 1941) is the Walter E. Koss Professor of [[Mathematics]] at [[Texas A&M University]].

==Academic biography==
DeVore received a B.S. from [[Eastern Michigan University]] in 1964 and a Ph.D. in [[mathematics]] from [[Ohio State University]] in 1967 under the supervision of Ranko Bojanic.<ref name="mg">{{mathgenealogy|name=Ronald Alvin DeVore|id=10109}}.</ref> From 1968 to 1977 he was at [[Oakland University]]. In 1977 he became a professor at the [[University of South Carolina]], where he served as the Robert L. Sumwalt Professor of Mathematics from 1986 to 2005. From 1999 to 2005 he also served as the director of the Industrial Mathematics Institutes, which he founded. In 2005 he retired from the [[University of South Carolina]]. Since 2008 he has been the Walter E. Koss Professor at [[Texas A&M University]] and will be named Distinguished Professor in Fall 2010.<ref name="current_cv">[http://www.math.tamu.edu/~rdevore/currentvitae.html Ronald A. DeVore Current Vitae]</ref>

DeVore has been a visiting professor at a number of universities around the world, including: [[Ohio State University]] (1967–1968), the [[University of Alberta]] (1971–1972), [[Universitat Erlangen-Nurnberg]] (1975–1976), [[Universitat Bonn]] (1977, 1978, 1979), [[Texas A&M University]] (1983), [[Scuola Normale di Pisa]] (1984), the [[University of Wisconsin]] (1983–1984, 1985, 1991), [[Purdue University]] (1990), the [[University of Paris VI]] (1996, 2000, 2002, 2004, 2005), [[Princeton University]] (1997–1998), [[RWTH Aachen University]] (2002), the [[University of Maryland]] (2004–2005), [[Rice University]] (2005–2006), the [[Courant Institute]] at [[New York University]] (2006–2007), and the Fondation Sciences Mathématiques de Paris (2009–2010).<ref name="current_cv" />

==Research==
DeVore has been active in the development of many areas of applied mathematics such as [[numerical analysis]] of [[partial differential equations]], [[machine learning]] algorithms, [[approximation theory|approximation]] of functions, [[wavelets|wavelet transforms]], and [[statistics]]. He has also made significant contributions to the theory of [[compressed sensing|compressive sensing]].

==Awards and honors==
DeVore has received numerous awards, including an [[Alexander von Humboldt]] Fellowship from 1975 to 1976, the Journal of Complexity Outstanding Paper Award in 2000, the Bulgarian Gold Medal of Science in 2001, the [[Humboldt Prize]] in 2002, the
ICS Hot Paper Award in 2003, an honorary doctorate from [[RWTH Aachen University]] in 2004,<ref>[http://www.igpm.rwth-aachen.de/www/Awards/award.html Honorary doctorate award for Prof. Ronald DeVore, Ph.D.], 2004.</ref> and the [[SPIE]] Wavelet Pioneer Award in 2007. He was also a plenary lecturer at the [[International Congress of Mathematicians]] in 2006.<ref>[http://icm2006.org/v_f/web_fr.php?PagIni=1pl Plenary Lectures], ICM, 2006.</ref>

In 2001 he became a member of the [[American Academy of Arts and Sciences]],<ref>[http://www.amacad.org/pdfs/alphaList09.pdf Alphabetical Index of Active Members], [[American Academy of Arts and Sciences]], 2009.</ref> and in 2007 he became a member of the [[Bulgarian Academy of Sciences]]. In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10.</ref>. From 2000 to 2002 he was the Chair of the society [[Foundations of Computational Mathematics]].

==References==
{{reflist}}

==External links==
*[http://www.math.tamu.edu/~rdevore/ DeVore's web page] at Texas A&M.

{{Authority control}}

{{Persondata 
| NAME = Devore, Ronald A.
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = May 14, 1941
| PLACE OF BIRTH = [[Detroit]], [[Michigan]]
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Devore, Ronald A.}}
[[Category:Living people]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Texas A&M University faculty]]
[[Category:Ohio State University alumni]]
[[Category:Purdue University faculty]]
[[Category:Rice University staff]]
[[Category:1941 births]]
[[Category:Eastern Michigan University alumni]]
[[Category:University of South Carolina faculty]]
[[Category:Oakland University faculty]]
[[Category:Fellows of the American Mathematical Society]]

Ronald DeVore

2015-07-28T12:45:22Z

Beltranc: /* Awards and honors */

{{Infobox scientist
| boxwidth =
| name = Ronald A. DeVore
| image = Ronald DeVore.jpg
| image_size =
| alt =
| caption =
| birth_date = May 14, 1941
| birth_place = [[Detroit]], [[Michigan]]
| residence =
| nationality = {{flagicon|US}} [[US|American]]
| fields = [[Mathematician]]
| workplaces = [[Texas A&M University]]
| alma_mater = [[Ohio State University]] [[Eastern Michigan University]]
| doctoral_advisor = Ranko Bojanic
| academic_advisors =
| doctoral_students =
| notable_students =
| known_for = [[Approximation theory]], [[Wavelet| Wavelet theory]], [[Compressed sensing|Compressive sensing]]
| awards = Member of [[Bulgarian Academy of Sciences]] (2007) 
[[SPIE]] Wavelet Pioneer Award (2007) 
Plenary Lecturer, [[International Congress of Mathematicians]] (2006) 
Honorary Doctorate, [[RWTH Aachen University]] (2004) 
[[Humboldt Prize]] (2002) 
Member of [[American Academy of Arts and Sciences]] (2001) 
Bulgarian Gold Medal of Science (2001) 
Journal of Complexity Outstanding Paper Award (2000)
}}

'''Ronald Alvin DeVore''' (born May 14, 1941) is the Walter E. Koss Professor of [[Mathematics]] at [[Texas A&M University]].

==Academic biography==
DeVore received a B.S. from [[Eastern Michigan University]] in 1964 and a Ph.D. in [[mathematics]] from [[Ohio State University]] in 1967 under the supervision of Ranko Bojanic.<ref name="mg">{{mathgenealogy|name=Ronald Alvin DeVore|id=10109}}.</ref> From 1968 to 1977 he was at [[Oakland University]]. In 1977 he became a professor at the [[University of South Carolina]], where he served as the Robert L. Sumwalt Professor of Mathematics from 1986 to 2005. From 1999 to 2005 he also served as the director of the Industrial Mathematics Institutes, which he founded. In 2005 he retired from the [[University of South Carolina]]. Since 2008 he has been the Walter E. Koss Professor at [[Texas A&M University]] and will be named Distinguished Professor in Fall 2010.<ref name="current_cv">[http://www.math.tamu.edu/~rdevore/currentvitae.html Ronald A. DeVore Current Vitae]</ref>

DeVore has been a visiting professor at a number of universities around the world, including: [[Ohio State University]] (1967–1968), the [[University of Alberta]] (1971–1972), [[Universitat Erlangen-Nurnberg]] (1975–1976), [[Universitat Bonn]] (1977, 1978, 1979), [[Texas A&M University]] (1983), [[Scuola Normale di Pisa]] (1984), the [[University of Wisconsin]] (1983–1984, 1985, 1991), [[Purdue University]] (1990), the [[University of Paris VI]] (1996, 2000, 2002, 2004, 2005), [[Princeton University]] (1997–1998), [[RWTH Aachen University]] (2002), the [[University of Maryland]] (2004–2005), [[Rice University]] (2005–2006), the [[Courant Institute]] at [[New York University]] (2006–2007), and the Fondation Sciences Mathématiques de Paris (2009–2010).<ref name="current_cv" />

==Research==
DeVore has been active in the development of many areas of applied mathematics such as [[numerical analysis]] of [[partial differential equations]], [[machine learning]] algorithms, [[approximation theory|approximation]] of functions, [[wavelets|wavelet transforms]], and [[statistics]]. He has also made significant contributions to the theory of [[compressed sensing|compressive sensing]].

==Awards and honors==
DeVore has received numerous awards, including an [[Alexander von Humboldt]] Fellowship from 1975 to 1976, the Journal of Complexity Outstanding Paper Award in 2000, the Bulgarian Gold Medal of Science in 2001, the [[Humboldt Prize]] in 2002, the
ICS Hot Paper Award in 2003, an honorary doctorate from [[RWTH Aachen University]] in 2004,<ref>[http://www.igpm.rwth-aachen.de/www/Awards/award.html Honorary doctorate award for Prof. Ronald DeVore, Ph.D.], 2004.</ref> and the [[SPIE]] Wavelet Pioneer Award in 2007. He was also a plenary lecturer at the [[International Congress of Mathematicians]] in 2006.<ref>[http://icm2006.org/v_f/web_fr.php?PagIni=1pl Plenary Lectures], ICM, 2006.</ref>

In 2001 he became a member of the [[American Academy of Arts and Sciences]],<ref>[http://www.amacad.org/pdfs/alphaList09.pdf Alphabetical Index of Active Members], [[American Academy of Arts and Sciences]], 2009.</ref> and in 2007 he became a member of the [[Bulgarian Academy of Sciences]]. In 2012 he became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10.</ref>. From 2000 to 2002 he was the Chair of [[Foundations of Computational Mathematics]].

==References==
{{reflist}}

==External links==
*[http://www.math.tamu.edu/~rdevore/ DeVore's web page] at Texas A&M.

{{Authority control}}

{{Persondata 
| NAME = Devore, Ronald A.
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = May 14, 1941
| PLACE OF BIRTH = [[Detroit]], [[Michigan]]
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Devore, Ronald A.}}
[[Category:Living people]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Texas A&M University faculty]]
[[Category:Ohio State University alumni]]
[[Category:Purdue University faculty]]
[[Category:Rice University staff]]
[[Category:1941 births]]
[[Category:Eastern Michigan University alumni]]
[[Category:University of South Carolina faculty]]
[[Category:Oakland University faculty]]
[[Category:Fellows of the American Mathematical Society]]

Arieh Iserles

2015-07-28T12:44:18Z

Beltranc:

{{Use dmy dates|date=December 2012}}
{{Use British English|date=December 2012}}
{{Infobox scientist
|name = Arieh Iserles
|image =
|birth_date = {{birth date and age|1947|09|02|df=y}}
|birth_place =
|death_date =
|death_place =
|residence = [[Cambridge, England]]
|citizenship =
|nationality =
|ethnicity =
|field =
|work_institutions = [[University of Cambridge]]
|alma_mater = [[Hebrew University of Jerusalem]], [[Ben-Gurion University of the Negev]]
|doctoral_advisor =
|doctoral_students =
|known_for =
|author_abbrev_bot =
|author_abbrev_zoo =
|influences =
|influenced =
|prizes =
|religion =
|footnotes =
|signature =
}}

'''Arieh Iserles''' (born 2 September 1947) is a [[computational mathematics|computational mathematician]], currently Professor of the Numerical Analysis of Differential Equations at the [[University of Cambridge]] and a member of the [[Faculty of Mathematics, University of Cambridge|Department of Applied Mathematics and Theoretical Physics]].

He studied at the [[Hebrew University of Jerusalem]] and [[Ben-Gurion University of the Negev]] and wrote his PhD dissertation on numerical methods for stiff ordinary differential equations. His research comprises many themes in computational and applied mathematics: ordinary and partial differential equations, approximation theory, geometric numerical integration, orthogonal polynomials, functional equations, computational dynamics and the computation of highly oscillatory phenomena.

He has written a textbook, ''A First Course in the Numerical Analysis of Differential Equations'' (Cambridge University Press, 2nd ed. 2009).<ref>http://www.cambridge.org/gb/knowledge/isbn/item2327165/?site_locale=en_GB</ref>

Arieh Iserles is the Managing Editor of [[Acta Numerica]], Editor-in-Chief of IMA Journal of Numerical Analysis<ref>http://imajna.oxfordjournals.org/</ref> and an editor of several other mathematical journals. From 1997 to 2000 he was the chair of the Society for [[Foundations of Computational Mathematics]].<ref>http://www.focm.net</ref>

He is currently a Director of the [http://www.maths.cam.ac.uk/postgrad/cca/ Cambridge Centre for Analysis (CCA)], an [[EPSRC]]-funded [[Doctoral Training Centre|Centre for Doctoral Training]] in [[mathematical analysis]].

In 1999, he was awarded the Onsager Medal, by the [[Norwegian University of Science and Technology]], in 2012 he received the [[David Crighton]] medal,<ref>http://www.ima.org.uk/about_us/awards_and_medals/david_crighton_medal.cfm</ref> presented by the [[Institute of Mathematics and its Applications]] and [[London Mathematical Society]] "for services to mathematics and the mathematics community"<ref>http://www.ima.org.uk/viewitem.cfm?cit_id=384309</ref> and in 2014 he was awarded by [[Society for Industrial and Applied Mathematics]] the SIAM Prize for Distinguished Service to the Profession.<ref>http://www.siam.org/prizes/sponsored/dist_service.php</ref> In 2012, Professor Iserles was an invited speaker at the 6th European Congress of Mathematics <ref>http://www.6ecm.pl/en</ref> in Kraków, 2–7 July 2012.

== External links ==
* [http://www.damtp.cam.ac.uk/user/na/people/Arieh/ Professor Iserles' website]

== References ==

{{Reflist}}

{{Persondata 
| NAME =Iserles, Arieh
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = British mathematician
| DATE OF BIRTH =2 September 1947
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Iserles, Arieh}}
[[Category:1947 births]]
[[Category:Living people]]
[[Category:Ben-Gurion University of the Negev alumni]]
[[Category:Hebrew University of Jerusalem alumni]]
[[Category:Mathematical analysts]]
[[Category:Members of the Department of Applied Mathematics and Theoretical Physics]]

{{UK-mathematician-stub}}

Michael Shub

2015-07-28T12:43:05Z

Beltranc: /* Biography */

{{Infobox person
| name = Michael Shub
| image = Michael Shub.jpg
| alt =
| caption = Michael Shub in April 2012
| birth_name = Michael Ira Shub
| birth_date = {{Birth date and age|1943|08|17}}
| birth_place =
| death_date = 
| death_place =
| nationality = USA
| other_names =
| occupation = mathematician, professor
| known_for = [[Blum Blum Shub]] [[pseudorandom number generator]]
| alma_mater = [[University of California, Berkeley]]
}}
'''Michael Ira Shub''' (born August 17, 1943) is an [[United States|American]] [[mathematician]] who has done research into [[Dynamical Systems]] and the Complexity of Real Number Algorithms.

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkeley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

Shub was the Chair of [[Foundations of Computational Mathematics]] from 1995 to 1997. In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>

== Work ==

Shub has produced publications in dynamical systems and in the complexity of real number algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps, which gave the first examples of structurally stable strange attractors. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems.<ref>Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref><ref>Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref><ref>Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator. see [[Blum Blum Shub]]. This is said to be useful from theoretical and practical perspectives. See.<ref>Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005</ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model is used to analyse the computability of functions.<ref>Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigorous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref>Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|author2=Blum, Manuel |author3=Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27–41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.<ref>{{cite journal|author=Robbin, Joel|title=Review: ''Global stability of dynamical systems'' by Michael Shub|journal=Bull. Amer. Math. Soc. (N.S.)|year=1988|volume=18|issue=2|pages=248–250|url=http://www.ams.org/journals/bull/1988-18-02/S0273-0979-1988-15665-0/S0273-0979-1988-15665-0.pdf|doi=10.1090/s0273-0979-1988-15665-0}}</ref>

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, July 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale [https://books.google.com/books/about/Complexity_and_Real_Computation.html?id=zxtrVqUP-AwC ''Complexity and Real Computation''] Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

{{Authority control|3=282048 |2=n85 |1=LCCN}}
{{Persondata
| NAME = Michael Ira Shub
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = August 17, 1943
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Shub, Michael Ira}}
[[Category:1943 births]]
[[Category:Living people]]
[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:University of California, Berkeley alumni]]

Foundations of Computational Mathematics

2015-07-28T12:41:59Z

Beltranc:

{{Infobox Organization
| name = Foundations of Computational Mathematics
| image = FoCM.png|thumb
| image_border =
| size = 150x150
| caption =
| formation = 1995
| type =
| headquarters =
| location =
| membership =
| language =
| leader_title = Chair
| leader_name = [[Wolfgang Dahmen]]
| key_people =
| num_staff =
| budget =
| website = http://focm-society.org/
}}

'''Foundations of Computational Mathematics''' ('''FoCM''') is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.

==Aim==
FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to:
*[[Approximation theory | Approximation Theory]]
*[[Algebraic_geometry#Computational_algebraic_geometry | Computational Algebraic Geometry]]
*Computational Dynamics
*Computational [[Harmonic analysis | Harmonic Analysis]], [[Image processing | Image]], and [[Signal processing | Signal Processing]]
*[[Computational number theory | Computational Number Theory]]
*[[Computational topology | Computational Topology]] and [[Computational geometry | Geometry]]
*[[Continuous optimization | Continuous Optimization]]
* Foundations of [[Numerical partial differential equations | Numerical PDE's]]
*[[Geometric integrator | Geometric Integration]] and [[Computational mechanics | Computational Mechanics]]
*[[Graph theory | Graph Theory]] and [[Combinatorics]]
*[[Information-based complexity | Information-based Complexity]]
*[[Online machine learning | Learning Theory ]]
*Multiresolution and Adaptivity in [[Numerical partial differential equations | Numerical PDE's]]
*[[Numerical linear algebra | Numerical Linear Algebra]]
*[[Random matrix | Random Matrices]]
*[[Analysis of algorithms | Real-Number Complexity]]
*[[Special functions | Special Functions]] and [[Orthogonal polynomials | Orthogonal Polynomials]]
*[[Stochastic computing | Stochastic Computing]]
*Symbolic Analysis

==History==
The Society for the Foundations of Computational Mathematics was launched in the Northern summer of 1995, following a month-long AMS–SIAM Summer Seminar in Park City, Utah, which was organized principally by [[Stephen Smale]]. That meeting hosted a number of sub-conferences on the frontier of Mathematics and Computation, focusing on many topics from numerical analysis and on the importance of a foundational theory of real number computation. The main thrust was on creating a shared intellectual space for activity bringing together computation and mathematics. During the final week at [[Michael Shub]]'s behest an informal lunch was arranged where Felipe Cucker, [[Arieh Iserles]], [[Narendra Karmarkar]], James Renegar, [[Michael Shub]] and [[Stephen Smale]] decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas. After a discussion, the name ''Foundations of Computational Mathematics'' was settled, and [[Michael Shub]] was chosen to lead the initiative with a little team formed by himself, [[Arieh Iserles]] and James Renegar.

The first FoCM conference took place in Rio de Janeiro and was hosted by IMPA with the support of its then-director [[Jacob Palis]]. Several conferences were organized later (see below), bringing together some of the world leading mathematicians and computer scientists, although the society was not formally established as a legal entity until 1999 simultaneously with the creation of the journal Foundations of Computational Mathematics. Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.

==Meetings==

The main FoCM conference is held every three years. Previous meetings include:

* Park City AMS—SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_prelim.html Announcement]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_panel.html Panel discussion].
* FoCM'97 (Rio de Janeiro, Brazil). [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_IOC.html International organizing committee]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_LOC.html Local organizing committee].
* FoCM'99 (Oxford, United Kingdom). [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_org.html Organizing committee] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_inv.html Plenary speakers.] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_wshops.html List of Workshops].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM02/ FoCM 2002] (Minneapolis, USA).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM05/ FoCM 2005] (Santander, Spain).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM08/ FoCM 2008] (Hong Kong, China).
* [http://www.damtp.cam.ac.uk/user/na/FoCM11/ FoCM 2011] (Budapest, Hungary).
* [https://www.fing.edu.uy/eventos/focm2014/ FoCM 2014] (Montevideo, Uruguay).

These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society, including:

* Foundations of Computational Mathematics Half Year Program, Berkeley, 1998, [[Mathematical Sciences Research Institute]]. [http://www.damtp.cam.ac.uk/user/na/FoCM/MSRI_organisers.html Organizing committee].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/HK.html Special Semester on Foundations of Computational Mathematics], Hong Kong, 1999, [[City University of Hong Kong]].
* [http://www.fields.utoronto.ca/programs/scientific/09-10/FoCM/index.html Thematic Program on the Foundations of Computational Mathematics], Toronto, 2009, [[Fields Institute]].
* [http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity A conference celebrating the work of] [[Michael Shub|Mike Shub]], Toronto, 2012 [[Fields Institute]].

==Publications==

Since january 2001, FoCM supports the [http://link.springer.com/journal/10208 Journal Foundations of Computational Mathematics]. Editors in Chief of the Journal:

* [[Michael Shub]] (2001–2002).
* [[Peter Olver]] (2002–2008).
* [[Arieh Iserles]] (2002–2011).
* Michael Todd (2008–2011).
* Felipe Cucker (2011–present).
* Albert Cohen (2014–present).

==Chairs==
The Chair of FoCM is elected every 3 years. This position has been held by various mathematicians worldwide.

* [[Michael Shub]] (1995–1997).
* [[Arieh Iserles]] (1997–2000).
* [[Ronald DeVore]] (2000–2002).
* [[Endre Süli]] (2002–2005).
* Michael Todd (2005–2008).
* Felipe Cucker (2008–2011).
* Teresa Krick (2011–2014).
* [[Wolfgang Dahmen]] (2014--).

==Stephen Smale Prize==

FoCM awards the "Stephen Smale Prize" whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Smale Prize recipients:

* Snorre H. Christiansen (2011). [http://focm-society.org/christiansen.php Laudatio].
* Carlos Beltrán and Mark Bravermann (2014). [http://focm-society.org/Beltran_and_Braverman.php Laudatio].

==External links==
*[http://focm-society.org/ the FoCM website]
*[http://link.springer.com/journal/10208 Journal FoCM website]

[[Category:Mathematical societies]]

Foundations of Computational Mathematics

2015-07-16T08:53:55Z

Beltranc: /* Meetings */

{{Under construction|notready=true}}
{{Infobox Organization
| name = Foundations of Computational Mathematics
| image = FoCM.png|thumb
| image_border =
| size = 150x150
| caption =
| formation = 1995
| type =
| headquarters =
| location =
| membership =
| language =
| leader_title = Chair
| leader_name = [[Wolfgang Dahmen]]
| key_people =
| num_staff =
| budget =
| website = http://focm-society.org/
}}

'''Foundations of Computational Mathematics''' ('''FoCM''') is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.

==Aim==
FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to:
*[[Approximation theory | Approximation Theory]]
*[[Algebraic_geometry#Computational_algebraic_geometry | Computational Algebraic Geometry]]
*Computational Dynamics
*Computational [[Harmonic analysis | Harmonic Analysis]], [[Image processing | Image]], and [[Signal processing | Signal Processing]]
*[[Computational number theory | Computational Number Theory]]
*[[Computational topology | Computational Topology]] and [[Computational geometry | Geometry]]
*[[Continuous optimization | Continuous Optimization]]
* Foundation of [[Numerical partial differential equations | Numerical PDE's]]
*[[Geometric integrator | Geometric Integration]] and [[Computational mechanics | Computational Mechanics]]
*[[Graph theory | Graph Theory]] and [[Combinatorics]]
*[[Information-based complexity | Information-based Complexity]]
*[[Online machine learning | Learning Theory ]]
*Multiresolution and Adaptivity in [[Numerical partial differential equations | Numerical PDE's]]
*[[Numerical linear algebra | Numerical Linear Algebra]]
*[[Random matrix | Random Matrices]]
*[[Analysis of algorithms | Real-Number Complexity]]
*[[Special functions | Special Functions]] and [[Orthogonal polynomials | Orthogonal Polynomials]]
*[[Stochastic computing | Stochastic Computing]]
*Symbolic Analysis

==History==
The Society for the Foundations of Computational Mathematics has been launched in the Northern summer of 1995, following a month-long AMS–SIAM Summer Seminar in Park City, Utah, which was organized principally by [[Stephen Smale]]. That meeting hosted a number of sub-conferences on the frontier of Mathematics and Computation, focusing on many topics from numerical analysis and on the importance of a foundational theory of real number computation. The main thrust was on creating a shared intellectual space for activity bringing together computation and mathematics. During the last week there was an informal lunch where Felipe Cucker, [[Arieh Iserles]], [[Narendra Karmarkar]], James Renegar, [[Michael Shub]] and [[Stephen Smale]] decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas. After a discussion, the name ''Foundations of Computational Mathematics'' was suggested by [[Arieh Iserles]], and [[Michael Shub]] was chosen to lead the initiative with a little team formed by himself, [[Arieh Iserles]] and James Renegar.

The first FoCM conference took place in Rio de Janeiro and was hosted by IMPA with the support of its then-director [[Jacob Palis]]. Several conferences were organized later (see below), bringing together some of the world leading mathematicians and computer scientists, although the society was not formally established as a legal entity until 2000 with the creation of the journal Foundations of Computational Mathematics. Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.

==Meetings==

The main FoCM conference is heald every three years. Previous meetings include:

* Park City AMS—SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_prelim.html Announcement]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_panel.html Panel discussion].
* FoCM'97 (Rio de Janeiro, Brazil). [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_IOC.html International organizing committee]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_LOC.html Local organizing committee].
* FoCM'99 (Oxford, United Kingdom). [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_org.html Organizing committee] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_inv.html Plenary speakers.] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_wshops.html List of Workshops].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM02/ FoCM 2002] (Minnesota, USA).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM05/ FoCM 2005] (Santander, Spain).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM08/ FoCM 2008] (Hong Kong, China).
* [http://www.damtp.cam.ac.uk/user/na/FoCM11/ FoCM 2011] (Budapest, Hungary).
* [https://www.fing.edu.uy/eventos/focm2014/ FoCM 2014] (Montevideo, Uruguay).

These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society, including:

* Foundations of Computational Mathematics Half Year Program, Berkeley, 1998, [[Mathematical Sciences Research Institute]]. [http://www.damtp.cam.ac.uk/user/na/FoCM/MSRI_organisers.html Organizing committee].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/HK.html Special Semester on Foundations of Computational Mathematics], Hong Kong, 1999, [[City University of Hong Kong]].
* [http://www.fields.utoronto.ca/programs/scientific/09-10/FoCM/index.html Thematic Program on the Foundations of Computational Mathematics], Toronto, 2009, [[Fields Institute]].
* [http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity A conference celebrating the work of] [[Michael Shub|Mike Shub]], Toronto, 2012 [[Fields Institute]].

==Publications==

Since january 2001, FoCM supports the [http://link.springer.com/journal/10208 Journal Foundations of Computational Mathematics]. Editors in Chief of the Journal:

* [[Michael Shub]] (2001–2002).
* [[Peter Olver]] (2002–2008).
* [[Arieh Iserles]] (2002–2011).
* Michael Todd (2008–2011).
* Felipe Cucker (2011–present).
* Albert Cohen (2014–present).

==Chairs==
The Chair of FoCM is elected every 3 years. This position has been held by various mathematicians worldwide.

* [[Michael Shub]] (1995–1997).
* [[Arieh Iserles]] (1997–2000).
* [[Ronald DeVore]] (2000–2002).
* [[Endre Süli]] (2002–2005).
* Michael Todd (2005–2008).
* Felipe Cucker (2008–2011).
* Teresa Krick (2011–2014).
* [[Wolfgang Dahmen]] (2014--).

==Stephen Smale Prize==

FoCM awards the "Stephen Smale Prize" whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Smale Prize recipients:

* Snorre H. Christiansen (2011). [http://focm-society.org/christiansen.php Laudatio].
* Carlos Beltrán and Mark Bravermann (2014). [http://focm-society.org/Beltran_and_Braverman.php Laudatio].

==External links==
*[http://focm-society.org/ the FoCM website]
*[http://link.springer.com/journal/10208 Journal FoCM website]

[[Category:Mathematical societies]]

Foundations of Computational Mathematics

2015-07-16T08:52:28Z

Beltranc:

{{Under construction|notready=true}}
{{Infobox Organization
| name = Foundations of Computational Mathematics
| image = FoCM.png|thumb
| image_border =
| size = 150x150
| caption =
| formation = 1995
| type =
| headquarters =
| location =
| membership =
| language =
| leader_title = Chair
| leader_name = [[Wolfgang Dahmen]]
| key_people =
| num_staff =
| budget =
| website = http://focm-society.org/
}}

'''Foundations of Computational Mathematics''' ('''FoCM''') is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.

==Aim==
FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to:
*[[Approximation theory | Approximation Theory]]
*[[Algebraic_geometry#Computational_algebraic_geometry | Computational Algebraic Geometry]]
*Computational Dynamics
*Computational [[Harmonic analysis | Harmonic Analysis]], [[Image processing | Image]], and [[Signal processing | Signal Processing]]
*[[Computational number theory | Computational Number Theory]]
*[[Computational topology | Computational Topology]] and [[Computational geometry | Geometry]]
*[[Continuous optimization | Continuous Optimization]]
* Foundation of [[Numerical partial differential equations | Numerical PDE's]]
*[[Geometric integrator | Geometric Integration]] and [[Computational mechanics | Computational Mechanics]]
*[[Graph theory | Graph Theory]] and [[Combinatorics]]
*[[Information-based complexity | Information-based Complexity]]
*[[Online machine learning | Learning Theory ]]
*Multiresolution and Adaptivity in [[Numerical partial differential equations | Numerical PDE's]]
*[[Numerical linear algebra | Numerical Linear Algebra]]
*[[Random matrix | Random Matrices]]
*[[Analysis of algorithms | Real-Number Complexity]]
*[[Special functions | Special Functions]] and [[Orthogonal polynomials | Orthogonal Polynomials]]
*[[Stochastic computing | Stochastic Computing]]
*Symbolic Analysis

==History==
The Society for the Foundations of Computational Mathematics has been launched in the Northern summer of 1995, following a month-long AMS–SIAM Summer Seminar in Park City, Utah, which was organized principally by [[Stephen Smale]]. That meeting hosted a number of sub-conferences on the frontier of Mathematics and Computation, focusing on many topics from numerical analysis and on the importance of a foundational theory of real number computation. The main thrust was on creating a shared intellectual space for activity bringing together computation and mathematics. During the last week there was an informal lunch where Felipe Cucker, [[Arieh Iserles]], [[Narendra Karmarkar]], James Renegar, [[Michael Shub]] and [[Stephen Smale]] decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas. After a discussion, the name ''Foundations of Computational Mathematics'' was suggested by [[Arieh Iserles]], and [[Michael Shub]] was chosen to lead the initiative with a little team formed by himself, [[Arieh Iserles]] and James Renegar.

The first FoCM conference took place in Rio de Janeiro and was hosted by IMPA with the support of its then-director [[Jacob Palis]]. Several conferences were organized later (see below), bringing together some of the world leading mathematicians and computer scientists, although the society was not formally established as a legal entity until 2000 with the creation of the journal Foundations of Computational Mathematics. Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.

==Meetings==

The main FoCM conference is heald every three years. Previous meetings include:

* Park City AMS—SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_prelim.html Announcement]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_panel.html Panel discussion].
* FoCM'97 (Rio de Janeiro, Brazil). [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_IOC.html International organizing committee]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_LOC.html Local organizing committee].
* FoCM'99 (Oxford, United Kingdom). [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_org.html Organizing committee] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_inv.html Plenary speakers.] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_wshops.html List of Workshops.] [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_workshops.html List of workshops].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM02/ FoCM 2002] (Minnesota, USA).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM05/ FoCM 2005] (Santander, Spain).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM08/ FoCM 2008] (Hong Kong, China).
* [http://www.damtp.cam.ac.uk/user/na/FoCM11/ FoCM 2011] (Budapest, Hungary).
* [https://www.fing.edu.uy/eventos/focm2014/ FoCM 2014] (Montevideo, Uruguay).

These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society, including:

* Foundations of Computational Mathematics Half Year Program, Berkeley, 1998, [[Mathematical Sciences Research Institute]]. [http://www.damtp.cam.ac.uk/user/na/FoCM/MSRI_organisers.html Organizing committee].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/HK.html Special Semester on Foundations of Computational Mathematics], Hong Kong, 1999, [[City University of Hong Kong]].
* [http://www.fields.utoronto.ca/programs/scientific/09-10/FoCM/index.html Thematic Program on the Foundations of Computational Mathematics], Toronto, 2009, [[Fields Institute]].
* [http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity A conference celebrating the work of] [[Michael Shub|Mike Shub]], Toronto, 2012 [[Fields Institute]].

==Publications==

Since january 2001, FoCM supports the [http://link.springer.com/journal/10208 Journal Foundations of Computational Mathematics]. Editors in Chief of the Journal:

* [[Michael Shub]] (2001–2002).
* [[Peter Olver]] (2002–2008).
* [[Arieh Iserles]] (2002–2011).
* Michael Todd (2008–2011).
* Felipe Cucker (2011–present).
* Albert Cohen (2014–present).

==Chairs==
The Chair of FoCM is elected every 3 years. This position has been held by various mathematicians worldwide.

* [[Michael Shub]] (1995–1997).
* [[Arieh Iserles]] (1997–2000).
* [[Ronald DeVore]] (2000–2002).
* [[Endre Süli]] (2002–2005).
* Michael Todd (2005–2008).
* Felipe Cucker (2008–2011).
* Teresa Krick (2011–2014).
* [[Wolfgang Dahmen]] (2014--).

==Stephen Smale Prize==

FoCM awards the "Stephen Smale Prize" whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Smale Prize recipients:

* Snorre H. Christiansen (2011). [http://focm-society.org/christiansen.php Laudatio].
* Carlos Beltrán and Mark Bravermann (2014). [http://focm-society.org/Beltran_and_Braverman.php Laudatio].

==External links==
*[http://focm-society.org/ the FoCM website]
*[http://link.springer.com/journal/10208 Journal FoCM website]

[[Category:Mathematical societies]]

Foundations of Computational Mathematics

2015-07-16T08:44:56Z

Beltranc: /* Stephen Smale Prize */

{{Under construction|notready=true}}
{{Infobox Organization
| name = Foundations of Computational Mathematics
| image = FoCM.png|thumb
| image_border =
| size = 150x150
| caption =
| formation = 1995
| type =
| headquarters =
| location =
| membership =
| language =
| leader_title = Chair
| leader_name = [[Wolfgang Dahmen]]
| key_people =
| num_staff =
| budget =
| website = http://focm-society.org/
}}

'''Foundations of Computational Mathematics''' ('''FoCM''') is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.

==Aim==
FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to:
*[[Approximation theory | Approximation Theory]]
*[[Algebraic_geometry#Computational_algebraic_geometry | Computational Algebraic Geometry]]
*Computational Dynamics
*Computational [[Harmonic analysis | Harmonic Analysis]], [[Image processing | Image]], and [[Signal processing | Signal Processing]]
*[[Computational number theory | Computational Number Theory]]
*[[Computational topology | Computational Topology]] and [[Computational geometry | Geometry]]
*[[Continuous optimization | Continuous Optimization]]
* Foundation of [[Numerical partial differential equations | Numerical PDE's]]
*[[Geometric integrator | Geometric Integration]] and [[Computational mechanics | Computational Mechanics]]
*[[Graph theory | Graph Theory]] and [[Combinatorics]]
*[[Information-based complexity | Information-based Complexity]]
*[[Online machine learning | Learning Theory ]]
*Multiresolution and Adaptivity in [[Numerical partial differential equations | Numerical PDE's]]
*[[Numerical linear algebra | Numerical Linear Algebra]]
*[[Random matrix | Random Matrices]]
*[[Analysis of algorithms | Real-Number Complexity]]
*[[Special functions | Special Functions]] and [[Orthogonal polynomials | Orthogonal Polynomials]]
*[[Stochastic computing | Stochastic Computing]]
*Symbolic Analysis

==History==
The Society for the Foundations of Computational Mathematics has been launched in the Northern summer of 1995, following a month-long AMS–SIAM Summer Seminar in Park City, Utah, which was organized principally by [[Stephen Smale]]. That meeting hosted a number of sub-conferences on the frontier of Mathematics and Computation, focusing on many topics from numerical analysis and on the importance of a foundational theory of real number computation. The main thrust was on creating a shared intellectual space for activity bringing together computation and mathematics. During the last week there was an informal lunch where Felipe Cucker, [[Arieh Iserles]], [[Narendra Karmarkar]], James Renegar, [[Michael Shub]] and [[Stephen Smale]] decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas. After a discussion, the name ''Foundations of Computational Mathematics'' was suggested by [[Arieh Iserles]], and [[Michael Shub]] was chosen to lead the initiative with a little team formed by himself, [[Arieh Iserles]] and James Renegar.

The first FoCM conference took place in Rio de Janeiro and was hosted by IMPA with the support of its then-director [[Jacob Palis]]. Several conferences were organized later (see below), bringing together some of the world leading mathematicians and computer scientists, although the society was not formally established as a legal entity until 2000 with the creation of the journal Foundations of Computational Mathematics. Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.

==Meetings==

The main FoCM conference is heald every three years. Previous meetings include:

* Park City AMS—SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_prelim.html Announcement]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_panel.html Panel discussion].
* FoCM'97 (Rio de Janeiro, Brazil). [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_IOC.html International organizing committee]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_LOC.html Local organizing committee].
* FoCM'99 (Oxford, United Kingdom). [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_org.html Organizing committee] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_inv.html Plenary speakers.] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_wshops.html List of Workshops.] [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_workshops.html List of workshops].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM02/ FoCM 2002] (Minnesota, USA).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM05/ FoCM 2005] (Santander, Spain).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM08/ FoCM 2008] (Hong Kong, China).
* [http://www.damtp.cam.ac.uk/user/na/FoCM11/ FoCM 2011] (Budapest, Hungary).
* [https://www.fing.edu.uy/eventos/focm2014/ FoCM 2014] (Montevideo, Uruguay).

These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society, including:

* Foundations of Computational Mathematics Half Year Program, Berkeley, 1998, [[Mathematical Sciences Research Institute]]. [http://www.damtp.cam.ac.uk/user/na/FoCM/MSRI_organisers.html Organizing committee].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/HK.html Special Semester on Foundations of Computational Mathematics], Hong Kong, 1999, [[City University of Hong Kong]].
* [http://www.fields.utoronto.ca/programs/scientific/09-10/FoCM/index.html Thematic Program on the Foundations of Computational Mathematics], Toronto, 2009, [[Fields Institute]].
* [http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity A conference celebrating the work of] [[Michael Shub|Mike Shub]], Toronto, 2012 [[Fields Institute]].

==Publications==

Since january 2001, FoCM supports the [http://link.springer.com/journal/10208 Journal Foundations of Computational Mathematics]. Editors in Chief of the Journal:

* [[Michael Shub]] (2001–2002).
* [[Peter Olver]] (2002–2008).
* [[Arieh Iserles]] (2002–2011).
* Michael Todd (2008–2011).
* Felipe Cucker (2011–present).
* Albert Cohen (2014–present).

==Chairs==
The Chair of FoCM is elected every 3 years. This position has been held by various mathematicians worldwide.

* [[Michael Shub]] (1995–1997).
* [[Arieh Iserles]] (1997–2000).
* [[Ronald DeVore]] (2000–2002).
* [[Endre Süli]] (2002–2005).
* Michael Todd (2005–2008).
* Felipe Cucker (2008–2011).
* Teresa Krick (2011–2014).
* [[Wolfgang Dahmen]] (2014--).

==Stephen Smale Prize==

FoCM awards the "Stephen Smale Prize" whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Smale Prize recipients:

* Snorre H. Christiansen (2011). [http://focm-society.org/christiansen.php Laudatio].
* Carlos Beltrán and Mark Bravermann (2014). [http://focm-society.org/Beltran_and_Braverman.php Laudatio].

==External links==
*[http://focm-society.org/ the FoCM website]
*[http://link.springer.com/journal/10208 Journal FoCM website]

[[Category:Mathematical societies]]

Foundations of Computational Mathematics

2015-07-16T08:43:52Z

Beltranc: /* Meetings */

{{Under construction|notready=true}}
{{Infobox Organization
| name = Foundations of Computational Mathematics
| image = FoCM.png|thumb
| image_border =
| size = 150x150
| caption =
| formation = 1995
| type =
| headquarters =
| location =
| membership =
| language =
| leader_title = Chair
| leader_name = [[Wolfgang Dahmen]]
| key_people =
| num_staff =
| budget =
| website = http://focm-society.org/
}}

'''Foundations of Computational Mathematics''' ('''FoCM''') is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.

==Aim==
FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to:
*[[Approximation theory | Approximation Theory]]
*[[Algebraic_geometry#Computational_algebraic_geometry | Computational Algebraic Geometry]]
*Computational Dynamics
*Computational [[Harmonic analysis | Harmonic Analysis]], [[Image processing | Image]], and [[Signal processing | Signal Processing]]
*[[Computational number theory | Computational Number Theory]]
*[[Computational topology | Computational Topology]] and [[Computational geometry | Geometry]]
*[[Continuous optimization | Continuous Optimization]]
* Foundation of [[Numerical partial differential equations | Numerical PDE's]]
*[[Geometric integrator | Geometric Integration]] and [[Computational mechanics | Computational Mechanics]]
*[[Graph theory | Graph Theory]] and [[Combinatorics]]
*[[Information-based complexity | Information-based Complexity]]
*[[Online machine learning | Learning Theory ]]
*Multiresolution and Adaptivity in [[Numerical partial differential equations | Numerical PDE's]]
*[[Numerical linear algebra | Numerical Linear Algebra]]
*[[Random matrix | Random Matrices]]
*[[Analysis of algorithms | Real-Number Complexity]]
*[[Special functions | Special Functions]] and [[Orthogonal polynomials | Orthogonal Polynomials]]
*[[Stochastic computing | Stochastic Computing]]
*Symbolic Analysis

==History==
The Society for the Foundations of Computational Mathematics has been launched in the Northern summer of 1995, following a month-long AMS–SIAM Summer Seminar in Park City, Utah, which was organized principally by [[Stephen Smale]]. That meeting hosted a number of sub-conferences on the frontier of Mathematics and Computation, focusing on many topics from numerical analysis and on the importance of a foundational theory of real number computation. The main thrust was on creating a shared intellectual space for activity bringing together computation and mathematics. During the last week there was an informal lunch where Felipe Cucker, [[Arieh Iserles]], [[Narendra Karmarkar]], James Renegar, [[Michael Shub]] and [[Stephen Smale]] decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas. After a discussion, the name ''Foundations of Computational Mathematics'' was suggested by [[Arieh Iserles]], and [[Michael Shub]] was chosen to lead the initiative with a little team formed by himself, [[Arieh Iserles]] and James Renegar.

The first FoCM conference took place in Rio de Janeiro and was hosted by IMPA with the support of its then-director [[Jacob Palis]]. Several conferences were organized later (see below), bringing together some of the world leading mathematicians and computer scientists, although the society was not formally established as a legal entity until 2000 with the creation of the journal Foundations of Computational Mathematics. Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.

==Meetings==

The main FoCM conference is heald every three years. Previous meetings include:

* Park City AMS—SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_prelim.html Announcement]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_panel.html Panel discussion].
* FoCM'97 (Rio de Janeiro, Brazil). [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_IOC.html International organizing committee]. [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_LOC.html Local organizing committee].
* FoCM'99 (Oxford, United Kingdom). [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_org.html Organizing committee] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_inv.html Plenary speakers.] [http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_wshops.html List of Workshops.] [http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_workshops.html List of workshops].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM02/ FoCM 2002] (Minnesota, USA).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM05/ FoCM 2005] (Santander, Spain).
* [http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM08/ FoCM 2008] (Hong Kong, China).
* [http://www.damtp.cam.ac.uk/user/na/FoCM11/ FoCM 2011] (Budapest, Hungary).
* [https://www.fing.edu.uy/eventos/focm2014/ FoCM 2014] (Montevideo, Uruguay).

These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society, including:

* Foundations of Computational Mathematics Half Year Program, Berkeley, 1998, [[Mathematical Sciences Research Institute]]. [http://www.damtp.cam.ac.uk/user/na/FoCM/MSRI_organisers.html Organizing committee].
* [http://www.damtp.cam.ac.uk/user/na/FoCM/HK.html Special Semester on Foundations of Computational Mathematics], Hong Kong, 1999, [[City University of Hong Kong]].
* [http://www.fields.utoronto.ca/programs/scientific/09-10/FoCM/index.html Thematic Program on the Foundations of Computational Mathematics], Toronto, 2009, [[Fields Institute]].
* [http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity A conference celebrating the work of] [[Michael Shub|Mike Shub]], Toronto, 2012 [[Fields Institute]].

==Publications==

Since january 2001, FoCM supports the [http://link.springer.com/journal/10208 Journal Foundations of Computational Mathematics]. Editors in Chief of the Journal:

* [[Michael Shub]] (2001–2002).
* [[Peter Olver]] (2002–2008).
* [[Arieh Iserles]] (2002–2011).
* Michael Todd (2008–2011).
* Felipe Cucker (2011–present).
* Albert Cohen (2014–present).

==Chairs==
The Chair of FoCM is elected every 3 years. This position has been held by various mathematicians worldwide.

* [[Michael Shub]] (1995–1997).
* [[Arieh Iserles]] (1997–2000).
* [[Ronald DeVore]] (2000–2002).
* [[Endre Süli]] (2002–2005).
* Michael Todd (2005–2008).
* Felipe Cucker (2008–2011).
* Teresa Krick (2011–2014).
* [[Wolfgang Dahmen]] (2014--).

==Stephen Smale Prize==

FoCM awards the "Stephen Smale Prize" whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Smale Prize recipients:

* Snorre H. Christiansen (2011).
* Carlos Beltrán and Mark Bravermann (2014).

==External links==
*[http://focm-society.org/ the FoCM website]
*[http://link.springer.com/journal/10208 Journal FoCM website]

[[Category:Mathematical societies]]

Foundations of Computational Mathematics

2015-07-16T08:42:19Z

Beltranc: /* Meetings */

{{Under construction|notready=true}}
{{Infobox Organization
| name = Foundations of Computational Mathematics
| image = FoCM.png|thumb
| image_border =
| size = 150x150
| caption =
| formation = 1995
| type =
| headquarters =
| location =
| membership =
| language =
| leader_title = Chair
| leader_name = [[Wolfgang Dahmen]]
| key_people =
| num_staff =
| budget =
| website = http://focm-society.org/
}}

'''Foundations of Computational Mathematics''' ('''FoCM''') is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.

==Aim==
FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to:
*[[Approximation theory | Approximation Theory]]
*[[Algebraic_geometry#Computational_algebraic_geometry | Computational Algebraic Geometry]]
*Computational Dynamics
*Computational [[Harmonic analysis | Harmonic Analysis]], [[Image processing | Image]], and [[Signal processing | Signal Processing]]
*[[Computational number theory | Computational Number Theory]]
*[[Computational topology | Computational Topology]] and [[Computational geometry | Geometry]]
*[[Continuous optimization | Continuous Optimization]]
* Foundation of [[Numerical partial differential equations | Numerical PDE's]]
*[[Geometric integrator | Geometric Integration]] and [[Computational mechanics | Computational Mechanics]]
*[[Graph theory | Graph Theory]] and [[Combinatorics]]
*[[Information-based complexity | Information-based Complexity]]
*[[Online machine learning | Learning Theory ]]
*Multiresolution and Adaptivity in [[Numerical partial differential equations | Numerical PDE's]]
*[[Numerical linear algebra | Numerical Linear Algebra]]
*[[Random matrix | Random Matrices]]
*[[Analysis of algorithms | Real-Number Complexity]]
*[[Special functions | Special Functions]] and [[Orthogonal polynomials | Orthogonal Polynomials]]
*[[Stochastic computing | Stochastic Computing]]
*Symbolic Analysis

==History==
The Society for the Foundations of Computational Mathematics has been launched in the Northern summer of 1995, following a month-long AMS–SIAM Summer Seminar in Park City, Utah, which was organized principally by [[Stephen Smale]]. That meeting hosted a number of sub-conferences on the frontier of Mathematics and Computation, focusing on many topics from numerical analysis and on the importance of a foundational theory of real number computation. The main thrust was on creating a shared intellectual space for activity bringing together computation and mathematics. During the last week there was an informal lunch where Felipe Cucker, [[Arieh Iserles]], [[Narendra Karmarkar]], James Renegar, [[Michael Shub]] and [[Stephen Smale]] decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas. After a discussion, the name ''Foundations of Computational Mathematics'' was suggested by [[Arieh Iserles]], and [[Michael Shub]] was chosen to lead the initiative with a little team formed by himself, [[Arieh Iserles]] and James Renegar.

The first FoCM conference took place in Rio de Janeiro and was hosted by IMPA with the support of its then-director [[Jacob Palis]]. Several conferences were organized later (see below), bringing together some of the world leading mathematicians and computer scientists, although the society was not formally established as a legal entity until 2000 with the creation of the journal Foundations of Computational Mathematics. Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.

==Meetings==

The main FoCM conference is heald every three years. Previous meetings include:

* Park City AMS—SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society. [[http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_prelim.html Announcement]]. [[http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_panel.html Panel discussion]].
* FoCM'97 (Rio de Janeiro, Brazil). [[http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_IOC.html International organizing committee]]. [[http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_LOC.html Local organizing committee]].
* FoCM'99 (Oxford, United Kingdom). [[http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_org.html Organizing committee]] [[http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_inv.html Plenary speakers.]] [[http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_wshops.html List of Workshops.]] [[http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_workshops.html List of workshops]].
* [[http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM02/ FoCM 2002]] (Minnesota, USA).
* [[http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM05/ FoCM 2005]] (Santander, Spain).
* [[http://www.damtp.cam.ac.uk/user/na/FoCM/FoCM08/ FoCM 2008]] (Hong Kong, China).
* [[http://www.damtp.cam.ac.uk/user/na/FoCM11/ FoCM 2011]] (Budapest, Hungary).
* [[https://www.fing.edu.uy/eventos/focm2014/ FoCM 2014]] (Montevideo, Uruguay).

These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society, including:

* Foundations of Computational Mathematics Half Year Program, Berkeley, 1998, [[Mathematical Sciences Research Institute]]. [[http://www.damtp.cam.ac.uk/user/na/FoCM/MSRI_organisers.html Organizing committee]].
* [[http://www.damtp.cam.ac.uk/user/na/FoCM/HK.html Special Semester on Foundations of Computational Mathematics]], Hong Kong, 1999, [[City University of Hong Kong]].
* [[http://www.fields.utoronto.ca/programs/scientific/09-10/FoCM/index.html Thematic Program on the Foundations of Computational Mathematics]], Toronto, 2009, [[Fields Institute]].
* [[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity A conference celebrating the work of]] [[Michael Shub|Mike Shub]], Toronto, 2012 [[Fields Institute]].

==Publications==

Since january 2001, FoCM supports the [http://link.springer.com/journal/10208 Journal Foundations of Computational Mathematics]. Editors in Chief of the Journal:

* [[Michael Shub]] (2001–2002).
* [[Peter Olver]] (2002–2008).
* [[Arieh Iserles]] (2002–2011).
* Michael Todd (2008–2011).
* Felipe Cucker (2011–present).
* Albert Cohen (2014–present).

==Chairs==
The Chair of FoCM is elected every 3 years. This position has been held by various mathematicians worldwide.

* [[Michael Shub]] (1995–1997).
* [[Arieh Iserles]] (1997–2000).
* [[Ronald DeVore]] (2000–2002).
* [[Endre Süli]] (2002–2005).
* Michael Todd (2005–2008).
* Felipe Cucker (2008–2011).
* Teresa Krick (2011–2014).
* [[Wolfgang Dahmen]] (2014--).

==Stephen Smale Prize==

FoCM awards the "Stephen Smale Prize" whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Smale Prize recipients:

* Snorre H. Christiansen (2011).
* Carlos Beltrán and Mark Bravermann (2014).

==External links==
*[http://focm-society.org/ the FoCM website]
*[http://link.springer.com/journal/10208 Journal FoCM website]

[[Category:Mathematical societies]]

Foundations of Computational Mathematics

2015-07-16T08:39:14Z

Beltranc: /* Meetings */

{{Under construction|notready=true}}
{{Infobox Organization
| name = Foundations of Computational Mathematics
| image = FoCM.png|thumb
| image_border =
| size = 150x150
| caption =
| formation = 1995
| type =
| headquarters =
| location =
| membership =
| language =
| leader_title = Chair
| leader_name = [[Wolfgang Dahmen]]
| key_people =
| num_staff =
| budget =
| website = http://focm-society.org/
}}

'''Foundations of Computational Mathematics''' ('''FoCM''') is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.

==Aim==
FoCM aims to explore the relationship between mathematics and computation, focusing both on the search for mathematical solutions to computational problems and computational solutions to mathematical problems. Topics of central interest in the Society include but are not restricted to:
*[[Approximation theory | Approximation Theory]]
*[[Algebraic_geometry#Computational_algebraic_geometry | Computational Algebraic Geometry]]
*Computational Dynamics
*Computational [[Harmonic analysis | Harmonic Analysis]], [[Image processing | Image]], and [[Signal processing | Signal Processing]]
*[[Computational number theory | Computational Number Theory]]
*[[Computational topology | Computational Topology]] and [[Computational geometry | Geometry]]
*[[Continuous optimization | Continuous Optimization]]
* Foundation of [[Numerical partial differential equations | Numerical PDE's]]
*[[Geometric integrator | Geometric Integration]] and [[Computational mechanics | Computational Mechanics]]
*[[Graph theory | Graph Theory]] and [[Combinatorics]]
*[[Information-based complexity | Information-based Complexity]]
*[[Online machine learning | Learning Theory ]]
*Multiresolution and Adaptivity in [[Numerical partial differential equations | Numerical PDE's]]
*[[Numerical linear algebra | Numerical Linear Algebra]]
*[[Random matrix | Random Matrices]]
*[[Analysis of algorithms | Real-Number Complexity]]
*[[Special functions | Special Functions]] and [[Orthogonal polynomials | Orthogonal Polynomials]]
*[[Stochastic computing | Stochastic Computing]]
*Symbolic Analysis

==History==
The Society for the Foundations of Computational Mathematics has been launched in the Northern summer of 1995, following a month-long AMS–SIAM Summer Seminar in Park City, Utah, which was organized principally by [[Stephen Smale]]. That meeting hosted a number of sub-conferences on the frontier of Mathematics and Computation, focusing on many topics from numerical analysis and on the importance of a foundational theory of real number computation. The main thrust was on creating a shared intellectual space for activity bringing together computation and mathematics. During the last week there was an informal lunch where Felipe Cucker, [[Arieh Iserles]], [[Narendra Karmarkar]], James Renegar, [[Michael Shub]] and [[Stephen Smale]] decided to go ahead and create a permanent entity that would organize periodic conferences covering subjects in the interplay between these two areas. After a discussion, the name ''Foundations of Computational Mathematics'' was suggested by [[Arieh Iserles]], and [[Michael Shub]] was chosen to lead the initiative with a little team formed by himself, [[Arieh Iserles]] and James Renegar.

The first FoCM conference took place in Rio de Janeiro and was hosted by IMPA with the support of its then-director [[Jacob Palis]]. Several conferences were organized later (see below), bringing together some of the world leading mathematicians and computer scientists, although the society was not formally established as a legal entity until 2000 with the creation of the journal Foundations of Computational Mathematics. Ever since, its main activities are its triennial meetings, special semesters and the support of the FoCM journal, as well as general advocacy of the mathematical areas underlying computation.

==Meetings==

The main FoCM conference is heald every three years. Previous meetings include:

* Park City AMS—SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society. [[http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_prelim.html Announcement]]. [[http://www.damtp.cam.ac.uk/user/na/FoCM/Utah_panel.html Panel discussion]].
* FoCM'97 (Rio de Janeiro, Brazil). [[http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_IOC.html International organizing committee]]. [[http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_LOC.html Local organizing committee]].
* FoCM'99 (Oxford, United Kingdom). [[http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_org.html Organizing committee]] [[http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_inv.html Plenary speakers.]] [[http://www.damtp.cam.ac.uk/user/na/FoCM/Oxford_wshops.html List of Workshops.]] [[http://www.damtp.cam.ac.uk/user/na/FoCM/Rio_workshops.html List of workshops]].
* FoCM 2002 (Minnesota, USA).
* FoCM 2005 (Santander, Spain).
* FoCM 2008 (Hong Kong, China).
* FoCM 2011 (Budapest, Hungary).
* FoCM 2014 (Montevideo, Uruguay).

These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society, including:

* Foundations of Computational Mathematics Half Year Program, Berkeley, 1998, [[Mathematical Sciences Research Institute]]
* Special Semester on Foundations of Computational Mathematics, Hong Kong, 1999, [[City University of Hong Kong]].
* Thematic Program on the Foundations of Computational Mathematics, Toronto, 2009, [[Fields Institute]].
* From Dynamics to Complexity A conference celebrating the work of [[Michael Shub|Mike Shub]], Toronto, 2012 [[Fields Institute]].

==Publications==

Since january 2001, FoCM supports the [http://link.springer.com/journal/10208 Journal Foundations of Computational Mathematics]. Editors in Chief of the Journal:

* [[Michael Shub]] (2001–2002).
* [[Peter Olver]] (2002–2008).
* [[Arieh Iserles]] (2002–2011).
* Michael Todd (2008–2011).
* Felipe Cucker (2011–present).
* Albert Cohen (2014–present).

==Chairs==
The Chair of FoCM is elected every 3 years. This position has been held by various mathematicians worldwide.

* [[Michael Shub]] (1995–1997).
* [[Arieh Iserles]] (1997–2000).
* [[Ronald DeVore]] (2000–2002).
* [[Endre Süli]] (2002–2005).
* Michael Todd (2005–2008).
* Felipe Cucker (2008–2011).
* Teresa Krick (2011–2014).
* [[Wolfgang Dahmen]] (2014--).

==Stephen Smale Prize==

FoCM awards the "Stephen Smale Prize" whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Smale Prize recipients:

* Snorre H. Christiansen (2011).
* Carlos Beltrán and Mark Bravermann (2014).

==External links==
*[http://focm-society.org/ the FoCM website]
*[http://link.springer.com/journal/10208 Journal FoCM website]

[[Category:Mathematical societies]]

Foundations of Computational Mathematics

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{{Infobox Organization
| name = Foundations of Computational Mathematics
| image = FoCM.png|thumb
| image_border =
| size = 150x150
| caption =
| formation = 1888
| type =
| headquarters =
| location =
| membership =
| language =
| leader_title = Chair
| leader_name = [[Wolfgang Dahmen|Wolfgang Dahmen]]
| key_people =
| num_staff =
| budget =
| website = [http://focm-society.org/]
}}
'''Foundations of Computational Mathematics''' ('''FoCM''') is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.

==History==
The Society for the Foundations of Computational Mathematics was created in the Northern summer of 1995, following the month-long meeting in Park City, Utah, which was principally organized by [[Stephen Smale]]. WRITE SOME MORE HISTORY HERE.

==Meetings==

The main FoCM conference is heald every three years. Previous meetings include:

* Park City AMS--SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society.
* FoCM'97 (Rio de Janeiro, Brazil).
* FoCM'99 (Oxford, United Kingdom).
* FoCM 2002 (Minnesota, USA).
* FoCM 2005 (Santander, Spain).
* FoCM 2008 (Hong Kong, China).
* FoCM 2011 (Budapest, Hungary).
* FoCM 2014 (Montevideo, Uruguay).

These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society.

==Publications==

FoCM supports one of the most relevant publications concerning Mathematics and Computation, the [http://link.springer.com/journal/10208|FoCM Journal].

==Prizes==

FoCM awards the "Stephen Smale Prize" whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Past winners are:

* Snorre H. Christiansen (2011).
* Carlos Beltrán and Mark Bravermann (2014).

==Chairs==
The Chair of FoCM is elected every 3 years.

* [[Arieh Iserles]] (1997--2000).
* [[Ronald DeVore]] (2000--2002).
* [[Endre Süli]] (2002--2005).
* Michael Todd (2005--2008).
* Felipe Cucker (2008--2011).
* Teresa Krick (2011--2014).
* [[Wolfgang Dahmen]] (2014--).

==External links==
*[http://focm-society.org/ the FoCM website]
*[http://link.springer.com/journal/10208|FoCM Journal]

[[Category:Mathematical societies]]

Foundations of Computational Mathematics

2015-07-13T09:36:22Z

Beltranc: ←Created page with '{{Infobox Organization | name = Foundations of Computational Mathematics | image = FoCM.png|thumb | image_border = | size = 150x150 | cap...'

{{Infobox Organization
| name = Foundations of Computational Mathematics
| image = FoCM.png|thumb
| image_border =
| size = 150x150
| caption =
| formation = 1888
| type =
| headquarters =
| location =
| membership = Membership in FoCM is free and available through this website.
| language =
| leader_title = Chair
| leader_name = [[Wolfgang Dahmen|Wolfgang Dahmen]]
| key_people =
| num_staff =
| budget =
| website = [http://focm-society.org/]
}}
'''Foundations of Computational Mathematics''' ('''FoCM''') is an international nonprofit organization that supports and promotes research at the interface of mathematics and computation. It fosters interaction among mathematics, computer science, and other areas of computational science through conferences, events and publications.

==History==
The Society for the Foundations of Computational Mathematics was created in the Northern summer of 1995, following the month-long meeting in Park City, Utah, which was principally organized by [[Stephen Smale]]. WRITE SOME MORE HISTORY HERE.

==Meetings==

The main FoCM conference is heald every three years. Previous meetings include:

* Park City AMS--SIAM 1995 Summer Seminar (Utah, USA), considered as the founding event of the society.
* FoCM'97 (Rio de Janeiro, Brazil).
* FoCM'99 (Oxford, United Kingdom).
* FoCM 2002 (Minnesota, USA).
* FoCM 2005 (Santander, Spain).
* FoCM 2008 (Hong Kong, China).
* FoCM 2011 (Budapest, Hungary).
* FoCM 2014 (Montevideo, Uruguay).

These conferences aim to cover the entire spectrum of mathematical computation. In addition to that, specialized events focusing on particular research topics are organized by the society.

==Publications==

FoCM supports one of the most relevant publications concerning Mathematics and Computation, the [http://link.springer.com/journal/10208|FoCM Journal].

==Prizes==

FoCM awards the "Stephen Smale Prize" whose objective is to recognize the work of a young mathematician in the areas at the heart of the society's interests and to help to promote his or her integration among the leaders of the scientific community. Past winners are:

* Snorre H. Christiansen (2011).
* Carlos Beltrán and Mark Bravermann (2014).

==Chairs==
The Chair of FoCM is elected every 3 years.

* [[Arieh Iserles]] (1997--2000).
* [[Ronald DeVore]] (2000--2002).
* [[Endre Süli]] (2002--2005).
* Michael Todd (2005--2008).
* Felipe Cucker (2008--2011).
* Teresa Krick (2011--2014).
* [[Wolfgang Dahmen]] (2014--).

==External links==
*[http://focm-society.org/ the FoCM website]
*[http://link.springer.com/journal/10208|FoCM Journal]

[[Category:Mathematical societies]]

Michael Shub

2014-02-19T16:02:38Z

Beltranc: /* Work */

[[File:Michael Shub.jpg|thumbnail|right|Michael Shub]]
'''Michael Ira Shub''' (born August 17, 1943) is an [[United States|American]] [[mathematician]] who has done research into [[Dynamical Systems]] and the Complexity of Real Number Algorithms.

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>

== Work ==

Shub has produced important publications in Dynamical Systems and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems.<ref>Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref><ref>Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref><ref>Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspectives, see.<ref>Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005</ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model became an extremely important tool to analyse the computability of functions.<ref>Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref>Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27–41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

{{Persondata
| NAME = Michael Ira Shub
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = August 17, 1943
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Shub, Michael Ira}}
[[Category:1943 births]]
[[Category:Living people]]
[[Category:American mathematicians]]
[[Category:University of California, Berkeley alumni]]

Michael Shub

2014-02-18T10:06:06Z

Beltranc:

[[File:Michael Shub.jpg|thumbnail|right|Michael Shub]]
'''Michael Ira Shub''' (born August 17, 1943) is an [[United States|American]] [[mathematician]] who has done research into [[Dynamical Systems]] and the Complexity of Real Number Algorithms.

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>

== Work ==

Shub has produced important publications in Dynamical Systems and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems.<ref>Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref><ref>Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref><ref>Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspectives, see.<ref>Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005</ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model as became a extremely important tool to analyse the computability of functions.<ref>Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref>Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27–41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

{{Persondata
| NAME = Michael Ira Shub
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = August 17, 1943
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Shub, Michael Ira}}
[[Category:1943 births]]
[[Category:Living people]]
[[Category:American mathematicians]]
[[Category:University of California, Berkeley alumni]]

Michael Shub

2014-02-18T10:04:42Z

Beltranc:

[[File:https://commons.wikimedia.org/wiki/File:Michael_Shub.jpg|thumbnail|right|Michael Shub (image downloaded from http://focm-society.org)]]
'''Michael Ira Shub''' (born August 17, 1943) is an [[United States|American]] [[mathematician]] who has done research into [[Dynamical Systems]] and the Complexity of Real Number Algorithms.

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>

== Work ==

Shub has produced important publications in Dynamical Systems and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems.<ref>Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref><ref>Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref><ref>Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspectives, see.<ref>Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005</ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model as became a extremely important tool to analyse the computability of functions.<ref>Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref>Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27–41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

{{Persondata
| NAME = Michael Ira Shub
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = August 17, 1943
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Shub, Michael Ira}}
[[Category:1943 births]]
[[Category:Living people]]
[[Category:American mathematicians]]
[[Category:University of California, Berkeley alumni]]

Michael Shub

2014-02-18T10:02:42Z

Beltranc:

[[File:http://focm-society.org/_images/img_mike_shub.jpg|thumbnail|right|Michael Shub (image downloaded from http://focm-society.org)]]
'''Michael Ira Shub''' (born August 17, 1943) is an [[United States|American]] [[mathematician]] who has done research into [[Dynamical Systems]] and the Complexity of Real Number Algorithms.

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>

== Work ==

Shub has produced important publications in Dynamical Systems and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems.<ref>Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref><ref>Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref><ref>Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspectives, see.<ref>Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005</ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model as became a extremely important tool to analyse the computability of functions.<ref>Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref>Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27–41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

{{Persondata
| NAME = Michael Ira Shub
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = August 17, 1943
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Shub, Michael Ira}}
[[Category:1943 births]]
[[Category:Living people]]
[[Category:American mathematicians]]
[[Category:University of California, Berkeley alumni]]

Michael Shub

2014-02-18T10:02:14Z

Beltranc:

[[File:/home/beltranc/tmp/img mike shub.jpg|thumbnail|right|Michael Shub (image downloaded from http://focm-society.org)]]
'''Michael Ira Shub''' (born August 17, 1943) is an [[United States|American]] [[mathematician]] who has done research into [[Dynamical Systems]] and the Complexity of Real Number Algorithms.

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>

== Work ==

Shub has produced important publications in Dynamical Systems and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems.<ref>Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref><ref>Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref><ref>Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspectives, see.<ref>Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005</ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model as became a extremely important tool to analyse the computability of functions.<ref>Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref>Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27–41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

{{Persondata
| NAME = Michael Ira Shub
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = American mathematician
| DATE OF BIRTH = August 17, 1943
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Shub, Michael Ira}}
[[Category:1943 births]]
[[Category:Living people]]
[[Category:American mathematicians]]
[[Category:University of California, Berkeley alumni]]

Lenore Blum

2014-02-17T17:53:34Z

Beltranc:

[[File:Lenore Blum.jpg|thumb|{{PAGENAME}}]]
'''Lenore Blum''' (December 18, 1942, [[New York City|New York]]) is a distinguished professor of Computer Science at [[Carnegie Mellon]]. She received her Ph.D. in [[mathematics]] from the [[Massachusetts Institute of Technology]] in 1968. Her dissertation was on Generalized Algebraic Structures and her advisor was [[Gerald Sacks]]. She then went to the [[University of California at Berkeley]] as a Postdoctoral Fellow and Lecturer in Mathematics. In 1973 she joined the faculty of [[Mills College]] where in 1974 she founded the Mathematics and [[Computer Science]] Department (serving as its Head or co-Head for 13 years). In 1979 she was awarded the first Letts-Villard Chair at Mills.

In 1983 Blum won an [[NSF CAREER]] award to work with [[Michael Shub]] for two years at the [[CUNY Graduate Center]]. They worked on secure random number generators and evaluating rational functions, see [[Blum Blum Shub]]. In 1987 she spent a year at [[IBM]]. In 1989 she published a paper with [[Michael Shub]] and [[Stephen Smale]] on [[NP completeness]], [[Recursion (computer science)|recursive functions]] and [[universal Turing machine]]s, see [[Blum–Shub–Smale machine]]. In 1990 she gave an address at the [[International Congress of Mathematicians]] on [[computational complexity theory]] and [[real computation]].
In 1992 Blum became the deputy director of the [[Mathematical Sciences Research Institute]], otherwise known as MSRI. After visiting the [[City University of Hong Kong]] for a year, she moved to her current position at [[Carnegie Mellon]] in 1999.
<ref>[http://www-2.cs.cmu.edu/~lblum/PAPERS/lblumShortVita.pdf]</ref> In 2002 she was selected to be a [[Noether Lecturer]]. In 2012 she became a fellow of the [[American Mathematical Society]].<ref>[http://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved 2012-11-10.</ref>

Lenore Blum is married to [[Manuel Blum]] and mother of [[Avrim Blum]]. All three are [[MIT alumni]] and professors of Computer Science at [[Carnegie Mellon]].

==Selected papers==
* L. Blum, M. Blum and M. Shub, “A Simple Secure Pseudo-Random Number Generator,” SIAM Journal of Computing, Vol. 15, No. 2, 364-383, May 1986.
* L. Blum, “A New Simple Homotopy Algorithm for Linear Programming I,” Journal of Complexity, Vol.4, No.2, 124-136, June 1988.
* L. Blum, M. Shub, S. Smale, “On a Theory of Computation Over the Real Numbers; NP Completeness, Recursive Functions and Universal Machines,” FOCS; 88; Bulletin of the AMS, Vol. 21, No.1, 1-46, July 1989.
* L. Blum, F. Cucker, M. Shub and S. Smale, Complexity and Real Computation, Springer-Verlag, 1998.
* L. Blum, “Computing over the Reals, Where Turing Meets Newton,” Notices of the AMS, October, 2004.<ref>[http://www.ams.org/mathscinet]</ref>

==References==
{{Reflist}}

==External links==
*[http://www-2.cs.cmu.edu/~lblum/ Lenore Blum's Home Page]
*[http://www.agnesscott.edu/lriddle/women/blum.htm "Lenore Blum", Biographies of Women Mathematicians], [[Agnes Scott College]]
*[http://www-history.mcs.st-andrews.ac.uk/Biographies/Blum.html Lenore Blum] from the [http://www-history.mcs.st-andrews.ac.uk/ MacTutor History of Mathematics archive]

{{Persondata
|NAME=Blum, Lenore
|ALTERNATIVE NAMES=
|SHORT DESCRIPTION= professor of Computer Science
|DATE OF BIRTH=
|PLACE OF BIRTH=
|DATE OF DEATH=
|PLACE OF DEATH=
}}
{{DEFAULTSORT:Blum, Lenore}}
[[Category:Carnegie Mellon University faculty]]
[[Category:Women mathematicians]]
[[Category:Living people]]
[[Category:Year of birth missing (living people)]]
[[Category:Fellows of the American Mathematical Society]]

Michael Shub

2014-02-17T17:51:19Z

Beltranc: /* Selected publications */

'''Michael Ira Shub''' (born August 17, 1943), is an [[American]] [[Mathematician]].

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>
== Work ==

Shub has produced important publications in [[Dynamical Systems]] and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref> Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems <ref> Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref> <ref> Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref>.<ref> Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspectives, see.<ref> Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005 </ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model as became a extremely important tool to analyse the computability of functions.<ref> Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref> Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27--41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub and S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==

* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.
{{Persondata
| NAME =
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION =
| DATE OF BIRTH = ,
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}

[[Category:Year of birth missing (living people)]]
[[Category:Living people]]
{{Improve categories|date=February 2014}}

Michael Shub

2014-02-17T17:47:41Z

Beltranc:

'''Michael Ira Shub''' (born August 17, 1943), is an [[American]] [[Mathematician]].

== Biography ==

Shub obtained his Ph.D. degree at the [[University of California, Berkley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at [[Brandeis University]], the [[University of California (Santa Cruz)]] and the [[Queens College at the City University of New York]]. From 1985 to 2004 he joined IBM's [[Thomas J. Watson Research Center]]. From 2004 to 2010 he worked at the [[University of Toronto]]. After 2010 he is a researcher at the [[University of Buenos Aires]] and at the City University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating his work.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Shub]''</ref>
== Work ==

Shub has produced important publications in [[Dynamical Systems]] and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref> Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems <ref> Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref> <ref> Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref>.<ref> Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>
He described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspectives, see.<ref> Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005 </ref>
In 1989 he proposed with [[Lenore Blum]] and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model as became a extremely important tool to analyse the computability of functions.<ref> Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>
In 1993, Shub and Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref> Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>
Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of their journal ''[[Foundations of Computational Mathematics]]'' with the same name until 2009.

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub,
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27--41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub et S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==

* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.
{{Persondata
| NAME =
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION =
| DATE OF BIRTH = ,
| PLACE OF BIRTH =
| DATE OF DEATH =
| PLACE OF DEATH =
}}

[[Category:Year of birth missing (living people)]]
[[Category:Living people]]
{{Improve categories|date=February 2014}}

Michael Shub

2014-02-12T17:09:19Z

Beltranc: /* Work */

{{AFC submission|||ts=20140120161711|u=Beltranc|ns=5}}
{{AFC submission|d|prof|declinets=20131031155356|decliner=Miniapolis|ts=20130926133310|u=Beltranc|ns=5}}{{AFC submission|d|v|declinets=20130823131518|decliner=Sionk|ts=20130808082108|u=Beltranc|ns=5|small=yes}}{{afc comment|1=Article's subject does not meet [[WP:ACADEMIC]]. [[User:Miniapolis|'''''Mini''''']] [[User talk:Miniapolis|'''''apolis''''']] 15:53, 31 October 2013 (UTC)}}

{{afc comment|1=Needs reliable secondary sources to back up these claims - papers and/or publications '''not''' by Mike Shub that say he's important [[User:Sionk|Sionk]] ([[User talk:Sionk|talk]]) 13:15, 23 August 2013 (UTC)}}

----

'''Michael Ira Shub''' (born August 17, 1943), is an [[American]] [[Mathematician]].

== Biography ==
Mike Shub obtained his Ph.D. degree at the University of California, Berkley entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at the Brandeis University, the University of California (Santa Cruz) and the Queens College at the City University of New York. From 1985 to 2004 he joined IBM's Thomas J. Watson Research Center. From 2004 to 2010 he worked at the Univesity of Toronto. After 2010 he is a researcher at the University of Buenos Aires and at the College University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating the work of Mike Shub.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Mike Shub]''</ref>

== Work ==
Mike Shub has produced important publications in Dynamical Systems and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref> Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems <ref> Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref> <ref> Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref>.<ref> Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>

Prof. Shub also described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspectives, see.<ref> Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005 </ref>

In 1989 he proposed with Lenore Blum and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model as became a extremely important tool to analyse the computability of functions.<ref> Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>

In 1993 Michael Shub and Stephen Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref> Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>

Prof. Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of the important journal with the same name until 2009. He has collaborated with up to 51 mathematicians, and his work has been cited over 2500 times (Source: MathScinet).

== Selected publications ==
{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub, Mike
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27--41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub et S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==
{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

Michael Shub

2014-02-12T16:13:10Z

Beltranc: /* Work */

{{AFC submission|||ts=20140120161711|u=Beltranc|ns=5}}
{{AFC submission|d|prof|declinets=20131031155356|decliner=Miniapolis|ts=20130926133310|u=Beltranc|ns=5}}{{AFC submission|d|v|declinets=20130823131518|decliner=Sionk|ts=20130808082108|u=Beltranc|ns=5|small=yes}}{{afc comment|1=Article's subject does not meet [[WP:ACADEMIC]]. [[User:Miniapolis|'''''Mini''''']] [[User talk:Miniapolis|'''''apolis''''']] 15:53, 31 October 2013 (UTC)}}

{{afc comment|1=Needs reliable secondary sources to back up these claims - papers and/or publications '''not''' by Mike Shub that say he's important [[User:Sionk|Sionk]] ([[User talk:Sionk|talk]]) 13:15, 23 August 2013 (UTC)}}

----

'''Michael Ira Shub''' (born August 17, 1943), is an [[American]] [[Mathematician]].

== Biography ==
Mike Shub obtained his Ph.D. degree at the University of California, Berkley entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at the Brandeis University, the University of California (Santa Cruz) and the Queens College at the City University of New York. From 1985 to 2004 he joined IBM's Thomas J. Watson Research Center. From 2004 to 2010 he worked at the Univesity of Toronto. After 2010 he is a researcher at the University of Buenos Aires and at the College University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating the work of Mike Shub.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Mike Shub]''</ref>

== Work ==
Mike Shub has produced important publications in Dynamical Systems and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref> Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems <ref> Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref> <ref> Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref>.<ref> Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>

Prof. Shub also described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspective, see.<ref> Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005 </ref>

In 1989 he proposed with Lenore Blum and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model as became a extremely important tool to analyse the computability of functions.<ref> Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>

In 1993 Michael Shub and Stephen Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades.<ref> Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>

Prof. Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of the important journal with the same name until 2009. He has collaborated with up to 51 mathematicians, and his work has been cited over 2500 times (Source: MathScinet).

== Selected publications ==
{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub, Mike
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27--41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub et S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==
{{Reflist}}

== External links ==
* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.

Michael Shub

2014-01-20T16:17:11Z

Beltranc:

{{AFC submission|d|prof|declinets=20131031155356|decliner=Miniapolis|ts=20130926133310|u=Beltranc|ns=5|small=yes}}{{AFC submission|d|v|declinets=20130823131518|decliner=Sionk|ts=20130808082108|u=Beltranc|ns=5}}
{{afc comment|1=Article's subject does not meet [[WP:ACADEMIC]]. [[User:Miniapolis|'''''Mini''''']][[User_talk:Miniapolis|'''''apolis''''']] 15:53, 31 October 2013 (UTC)}}

{{afc comment|1=Needs reliable secondary sources to back up these claims - papers and/or publications '''not''' by Mike Shub that say he's important [[User:Sionk|Sionk]] ([[User talk:Sionk|talk]]) 13:15, 23 August 2013 (UTC)}}

----

'''Michael Ira Shub''' (born August 17, 1943), is an [[American]] [[Mathematician]].

== Biography ==

Mike Shub obtained his Ph.D. degree at the University of California, Berkley entitled ''Endomorphisms of Compact Differentiable Manifolds'' on 1967. His advisor was [[Stephen Smale]].<ref>{{MathGenealogy|32568|Michael Ira Shub}}</ref>
From 1967 to 1985 he worked at the Brandeis University, the University of California (Santa Cruz) and the Queens College at the City University of New York. From 1985 to 2004 he joined IBM's Thomas J. Watson Research Center. From 2004 to 2010 he worked at the Univesity of Toronto. After 2010 he is a researcher at the University of Buenos Aires and at the College University of New York.

In 2012, a conference ''From Dynamics to Complexity'' was organised at the Fields Institute in [[Toronto]] celebrating the work of Mike Shub.<ref>''[http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ From Dynamics to Complexity - A conference celebrating the work of Mike Shub]''</ref>
== Work ==

Mike Shub has produced important publications in Dynamical Systems and in the Complexity of Real Number Algorithms. In his Ph.D. in 1967 he introduced the notion of expanding maps. In 1974 he proposed the Entropy Conjecture, an important open problem in Dynamical Systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref> Y. Yomdin, ''[http://link.springer.com/article/10.1007%2FBF02766215#page-1 Volume growth and entropy.]'', Israel J. Math. 57, no. 3, 1987.</ref> This same year Michael Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advances books on the subject of Dynamical Systems <ref> Devaney, R. ''A first course in chaotic dynamical systems'', Westview Press, 1992.</ref> <ref> Wiggins, S. ''Introduction to applied nonlinear systems and chaos'', Springer, 1990.</ref> <ref> Hasselblatt , B. and Katok, A. ''Handbook of dynamical systems, Vol I'', Elsevier, 2002.</ref>.

Prof. Shub also described jointly with Lenore and Manuel Blum a simple, unpredictable, secure random number generator, see [[Blum Blum Shub]], which is considered an important landmark both from theoretical and practical perspective and is described in some of the most widely used cryptography manuals, see <ref> Stinson, D. ''Cryptography: Theory and Practice, Third Edition'', Taylor and Francis, 2005 </ref>.

In 1989 he proposed with Lenore Blum and Stephen Smale the notion of [[Blum–Shub–Smale machine]], an alternative to the classical Turing model of computation. Their model as became a extremely important tool to analyse the computability of functions <ref> Gradel, E. [http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf Finite Model Theory and Its Applications], Springer-Verlag, 2007</ref>.

In 1993 Michael Shub and Stephen Smale initiated a rigurous analysis of homotopy-based algorithms for solving systems of nonlinear algebraic equations which has inspired much of the work in that area during the last two decades <ref> Bürgisser, P. and Cucker, F.''Condition: The Geometry of Numerical Algorithms'', Springer, 2013</ref>.

Prof. Shub was one of the founders of the nonprofit association Foundations of Computational Mathematics, and editor of the important journal with the same name until 2009. He has collaborated with up to 51 mathematicians, and his work has been cited over 2500 times (Source: MathScinet).

== Selected publications ==

{{cite journal
|last=Blum
|first=Lenore
|coauthors=Blum, Manuel; Shub, Mike
|title=A Simple Unpredictable Pseudo-Random Number Generator
|journal=SIAM Journal on Computing
|date=1 May 1986
|volume=15
|issue=2
|pages=364–383
|doi=10.1137/0215025
|url=http://epubs.siam.org/doi/abs/10.1137/0215025}}

M. Shub, ''[http://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf Dynamical Systems, filtrations and entropy]'', Bulletin of the American Mathematical Society 80, 1974, pp. 27--41.

M. Shub, ''Global Stability of Dynamical Systems'', Springer-Berlag: New York, Heidelberg, Berlin, 1987.

L. Blum, M. Shub et S. Smale, ''[http://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines]'', Bulletin of the American Mathematical Society, juillet 1989.

M. Shub and S. Smale ''[http://www.jstor.org/stable/2152805 Complexity of Bezout's Theorem I: Geometric Aspects]'', Journal of the American Mathematical Society, volume 6, number 2, 1993.

L. Blum, F. Cucker, M. Shub and S. Smale ''Complexity and Real Computation'' Springer-Berlag: New York, Heidelberg, Berlin, 1997.

== References ==

{{Reflist}}

== External links ==

* [http://www.math.toronto.edu/shub/ Personal website] at the University of Toronto.


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Michael Shub

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