UW-PIMS Mathematics Colloquium: Rekha Thomas

  • Date: 04/29/2011
Rekha Thomas

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 called 
"convex algebraic geometry."

Other Information: 

Location: Raitt Hall, Room 121


Fore more information please visit University of Washington Department of Mathematics