Professor Felipe Cucker will present a colloquium on Smale's 17th Problem on Friday 13 May 2011, at 16:10 in Lecture Theatre C of the James Clerk Maxwell Building. The colloquium will be followed by a wine reception.

### Smale's 17th Problem

At the request of the International Mathematical Union, in 1999, Steve Smale proposed a list of 18 problems for the mathematicians of the 21st century. The 17th of these problems asks for the existence of a deterministic algorithm computing an approximate solution of a system of n complex polynomials in n unknowns in time polynomial, on the average, in the size N of the input system. The talk gives fundamental advances in this problem including the smoothed analysis of a randomized algorithm and a deterministic algorithm working in near-polynomial average time.

### About the Speaker

Felipe Cucker is Chair Professor of Mathematics at the City University of Hong Kong. He has contributed ground-breaking research in a wide variety of fields such as computational complexity theory, foundations of optimization and numerical analysis, real algebraic geometry, learning theory, language evolution, dynamics of flocking, and probability theory. Among his books are Complexity and Real Computation (with Lenore Blum, Steve Smale, and Mike Shub), Mathematical Foundations of Learning, and an upcoming treatise on Mathematics and the Arts.

Prof. Cucker is currently the chairman of the Society for the Foundations of Computational Mathematics and is a member of Barcelona's Royal Academy of Sciences and Arts.