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Michael Shub

Faculty and Staff Profiles

Michael Shub

Martin and Michele Cohen Professor, Chair

North Academic Center 8/201
Phone Number: 

Michael Shub began his mathematical career as a dynamicist. In his thesis he defined and laid the groundwork for the classification of expanding maps In the hands of his advisor, Steve Smale, these maps provided the first examples of structurally stable strange attractors,  thus contributing in an essential way to the revolution in dynamical systems theory now known as chaos theory and the relationship of this theory to turbulence. In dynamics he proceeded to study the relations between smooth dynamics and algebraic topology formulating the entropy conjecture and proving a variety of theorems on this theme. The conjecture was ultimately proven by Yomdin.  In more recent years he has worked with Charles Pugh on the extent that chaotic dynamical systems may be understood statistically..

In 1981 he began working with Steve Smale on the complexity theory of solving first one and then a system of polynomial equations.  With Lenore Blum they initiated a general theory of complexity of computation over the reals -or complex numbers -or indeed any ring or field- thus generalizing the classical theory of Turing and problems such as does P =NP? to the real and complex numbers, which are the natural domains for the algorithms of scientific and engineering computations. Along the way, Shub with Lenore and Manuel Blum  proposed a pseudo-random number generator now called BBS and proved it cryptographically secure.

Shub has had positions at Brandeis University, the University of  California at Santa Cruz, The City University of New York, IBM Research, the University of Toronto, and the Argentine CONICET . He is a Fellow of the American Association for the Advancement of Science, the New York Academy of Science, the Fields Institute, the AmericanMathematical Society and is on the Fulbright Specialist Roster.   He has given invited talks to the American, Australian and Spanish mathematics societies as well to SIAM and the International Congress of Mathematicians.

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