Michael Shub

{{short description|American mathematician}} {{Infobox scientist | 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 = | other_names = | fields = [[Mathematics]] | known_for = [[Blum Blum Shub]] [[pseudorandom number generator]] | alma_mater = [[University of California, Berkeley]] | work_institution = [[Brandeis University]] [[University of California, Santa Cruz]] [[Queens College at the City University of New York]] [[Thomas J. Watson Research Center]] [[University of Toronto]] [[University of Buenos Aires]] }} '''Michael Ira Shub''' (born August 17, 1943) is an [[Americans|American]] [[mathematician]] who has done research into [[dynamical systems]] and the complexity of [[real number]] algorithms.

==Career== ===1967: Ph.D. and early career=== In 1967, Shub obtained his [[Ph.D.]] degree at the [[University of California, Berkeley]] with a thesis entitled ''Endomorphisms of Compact Differentiable Manifolds''. In his Ph.D. thesis, he introduced the notion of expanding maps, which gave the first examples of structurally stable strange attractors. 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]]. In 1974, he proposed the Entropy Conjecture, an open problem in dynamical systems, which was proved by Yosef Yomdin for <math>C^\infty</math> mappings in 1987.<ref>{{cite journal |last=Yomdin |first=Yosef |date=October 1987 |title=Volume growth and entropy |journal=[[Israel Journal of Mathematics]] |location=Jerusalem, Israel |publisher=[[Hebrew University of Jerusalem]] |volume=57 |issue=3 |pages=285–300 |doi=10.1007/BF02766215 |doi-access=free |s2cid=121442787}}</ref>

===1985–2004: IBM research=== From 1985 to 2004, he joined [[IBM]]'s [[Thomas J. Watson Research Center]]. In 1987, Shub published his book ''Global Stability of Dynamical Systems'', which is often used as a reference in introductory and advanced books on the subject of dynamical systems.<ref>{{cite book |last=Devaney |first=Robert L. |title=A First Course in Chaotic Dynamical Systems |publisher=[[Westview Press]] |year=1992 |isbn=9780429983115 |location=Boulder, Colorado |pages=14–127 |authorlink=Robert L. Devaney}}</ref><ref>{{cite book |last=Wiggin |first=Stephen |title=Introduction to Applied Nonlinear Systems and Chaos |date=1990 |publisher=[[Springer-Verlag]] |isbn=978-0387001777 |location=New York City |page=470}}</ref><ref>{{cite book |last1=Hasselblatt |first1=Boris |title=Handbook of Dynamical Systems, Vol I |last2=Katok |first2=Anatole |date=2002 |publisher=[[Elsevier]] |isbn=0444826696 |location=Amsterdam, Netherlands |page=69 |authorlink2=Anatole Katok}}</ref> In 1993, Shub and Stephen 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>{{cite book |last1=Bürgisser |first1=Peter |title=Condition: The Geometry of Numerical Algorithms |last2=Cucker |first2=Felipe |date=2013 |publisher=[[Springer-Verlag]] |isbn=978-3-642-38895-8 |location=New York City |page=283}}</ref>

From 1995 to 1997, Shub was the founding chair of the [[Foundations of Computational Mathematics|Society for the Foundations of Computational Mathematics]]. In 2001, Shub became a founding editor of their journal, ''Foundations of Computational Mathematics''.<ref name=":0">{{Cite web |last=York |first=The City College of New |date=2016-09-06 |title=Michael Shub |url=https://www.ccny.cuny.edu/profiles/michael-shub |access-date=2023-02-21 |website=The City College of New York |language=en-us}}</ref>

====1986: Blum Blum Shub==== {{Full article|Blum Blum Shub}} Shub, along with coauthors Lenore and Manuel Blum, described a simple, unpredictable, secure [[random number generator]] (see [[Blum Blum Shub]]). This random generator is useful from theoretical and practical perspectives.<ref>{{cite book |last=Stinson |first=Douglas R. |title=Cryptography: Theory and Practice, Third Edition |date=2005 |publisher=[[Taylor & Francis]] |isbn=978-1584885085 |location=Oxfordshire, England |page=336}}</ref>

====1989: Blum–Shub–Smale machine==== {{Full article|Blum–Shub–Smale machine}} 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>{{cite book |last=Grädel |first=Erich |url=http://www.logic.rwth-aachen.de/pub/graedel/FMTbook-Chapter3.pdf |title=Finite Model Theory and Its Applications |date=2007 |publisher=[[Springer-Verlag]] |location=New York City |page=217 |chapter=Algorithmic Model Theory}}</ref>

===2004–2010: Post-IBM=== From 2004 to 2010, he worked at the [[University of Toronto]].<ref name=":0" /> After 2010, he became a researcher at the [[University of Buenos Aires]] and at the [[Graduate Center, CUNY|Graduate Center of the City University of New York]].<ref name=":0" /> Since 2016, he has been Martin and Michele Cohen Professor and Chair of the Mathematics Department at [[City College of New York]].<ref name=":0" />

==Awards and recognition== *1972: Fellow of [[Alfred P. Sloan Foundation]].<ref name=":1">{{Cite web |title=Michael Shub: H-index & Awards - Academic Profile {{!}} Research.com |url=https://research.com/u/michael-shub |access-date=2023-02-21 |website=Research.com |language=en-US}}</ref> *2000: Fellow of the [[American Association for the Advancement of Science]].<ref name=":1" /> *2012: A conference, ''From Dynamics to Complexity'', was organized at the [[Fields Institute]] in Toronto celebrating his work.<ref>{{cite conference |date=May 7–11, 2012 |title=From Dynamics to Complexity - A conference celebrating the work of Shub |url=http://www.fields.utoronto.ca/programs/scientific/11-12/dynamics2complexity/ |location=Toronto, Ontario, Canada |publisher=[[Fields Institute]]}}</ref> *2015: Fellow of the [[American Mathematical Society]] "for contributions to smooth dynamics and to complexity theory."<ref>{{cite web |title=2016 Class of the Fellows of the AMS |url=https://www.ams.org/profession/ams-fellows/new-fellows |access-date=November 16, 2015 |publisher=[[American Mathematical Society]]}}</ref> * 2016: [[Fulbright Program#Scholar grants|Fulbright Specialist]].<ref name=":0" />

==Selected publications== *{{cite journal |last1=Blum|first1=Lenore |last2=Blum|first2= Manuel |last3=Shub|first3=Michael |title=A Simple Unpredictable Pseudo-Random Number Generator |journal=[[SIAM Journal on Computing]] |publisher=[[Society for Industrial and Applied Mathematics]] |location=Philadelphia, Pennsylvania |date=1 May 1986 |volume=15 |issue=2 |pages=364–383 |doi=10.1137/0215025}} *{{cite journal| first=Michael| last= Shub| url=https://www.ams.org/bull/1974-80-01/S0002-9904-1974-13344-6/S0002-9904-1974-13344-6.pdf| title= Dynamical systems, filtrations and entropy| journal= [[Bulletin of the American Mathematical Society]] | publisher=[[American Mathematical Society]]| location=Providence, Rhode Island| volume= 80| year=1974| pages=27–41| doi= 10.1090/S0002-9904-1974-13344-6| doi-access= free}} *{{cite book| first=Michael| last=Shub| title=Global Stability of Dynamical Systems| publisher=[[Springer-Verlag]]| location=New York City| date=1987| isbn=978-0387962955}} *{{cite journal| first=Joel| last=Robbin| title=Review: ''Global stability of dynamical systems'' by Michael Shub| journal=[[Bulletin of the American Mathematical Society]]| publisher=[[American Mathematical Society]]| location=Providence, Rhode Island| date=1988| volume=18| issue=2| pages=248–250| url=https://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| doi-access=free}} *{{cite journal| first1=Lenore| last1=Blum| first2=Michael| last2=Shub| first3=Stephen| last3=Smale| url=https://www.ams.org/bull/1989-21-01/S0273-0979-1989-15750-9/S0273-0979-1989-15750-9.pdf| title=On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines| journal=[[Bulletin of the American Mathematical Society]]| publisher=[[American Mathematical Society]]| location=Providence, Rhode Island| date=July 1989| volume=21| pages=1–47| doi=10.1090/S0273-0979-1989-15750-9| doi-access=free}} *{{cite journal| first1=Michael| last1= Shub| first2=Stephen| last2= Smale| authorlink2=Stephen Smale| jstor=2152805| title= Complexity of Bézout's Theorem I: Geometric Aspects| journal= [[Journal of the American Mathematical Society]] | publisher=[[American Mathematical Society]]| location=Providence, Rhode Island| volume =6| issue= 2| date= 1993| pages=459–501| doi=10.2307/2152805}} *{{cite book| first1=Lenore| last1=Blum| first2=Felipe| last2=Cucker| first3=Michael|last3=Shub| first4=Stephen| last4=Smale| title=[[Complexity and Real Computation]]| publisher=[[Springer-Verlag]]| location=New York City| date=1997| isbn=978-0387982816}}

==References== {{Reflist|2}}

==External links== *[https://web.archive.org/web/20180417105227/https://shub.ccny.cuny.edu/ Personal website] at the City College of New York.

{{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]] [[Category:Fellows of the American Mathematical Society]] [[Category:Brandeis University faculty]] [[Category:CUNY Graduate Center faculty]] [[Category:City College of New York faculty]] [[Category:University of California, Santa Cruz faculty]] [[Category:Academic staff of the University of Toronto]] [[Category:Academic staff of the University of Buenos Aires]] [[Category:IBM Research computer scientists]] [[Category:Queens College, City University of New York faculty]]