Michael Shub

Michael Ira Shub (born August 17, 1943) is an 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.
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 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.

In 2015 he was elected as a fellow of the American Mathematical Society "for contributions to smooth dynamics and to complexity theory."

Since August 2016, he has been Martin and Michele Cohen Professor and Chair of the Mathematics Department at City College of New York.

Work

Shub has produced publications in dynamical systems and in the complexity of real number algorithms. In his Ph.D. thesis 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 open problem in dynamical systems, which was proved by Yosef Yomdin for $C^\infty$ mappings in 1987.

This same year, 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. 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.
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.
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.
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

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References

External links

Personal website
at the City College of New York.

{{DEFAULTSORT:Shub, Michael Ira
1943 births
Living people
20th-century American mathematicians
21st-century American mathematicians
University of California, Berkeley alumni
Fellows of the American Mathematical Society
Brandeis University faculty
City University of New York faculty
Graduate Center, CUNY faculty
City College of New York faculty
University of California, Santa Cruz faculty
University of Toronto faculty
University of Buenos Aires faculty
IBM Research computer scientists