## UW-PIMS Mathematics Colloquium: Rekha Thomas

- Date: 04/29/2011

University of Washington

From Hilbert's 17th problem to polynomial optimization and convex algebraic geometry

Polynomial optimization concerns minimizing a polynomial subject to

polynomial equations and inequalities. While this is a natural model for

many applications, there are many difficulties (usually numerical and

algorithmic) that have prevented their wide-spread use. However, in the last

10 years, several research streams in math and engineering have come

together to breathe new life into this important class of problems. The

story starts with Hilbert's work on nonnegative polynomials, but then goes

on to use ideas from many branches of mathematics such as real algebraic

geometry, convex analysis, functional analysis, optimization, probability

and combinatorics. In particular, this is an area where algebra and analysis

become naturally intertwined. I will attempt a (biased) survey of the main

ideas that has helped in this development and defined a new field calledÂ

"convex algebraic geometry."

Location: Raitt Hall, Room 121

Fore more information please visit University of Washington Department of Mathematics