2008-2009 Milliman Lectures
Department of Mathematics
University of Washington

ANDREI OKOUNKOV
Professor of Mathematics
Princeton University

May 19th, 20th, and 21st
4:00 - 5:00pm
Sieg Hall, Room 134

Applied Noncommutative Projective Geometry

Abstract: Noncommutative projective geometry deals with noncommutative algebras that, in a certain technical sense, are just as good as polynomials.

Their study was begun by M. Artin and W. Schelter over twenty years ago and grew into a rich and fascinating subject since. In these lectures, I will explain some applications of this theory to such basic mathematical objects as linear difference equations. These difference equations are of direct probabilistic interest (which will be also explained in the lectures) and thus noncommutative algebraic surfaces shed light on the behavior of random stepped surfaces.

View a streaming video of Lecture I using the free RealPlayer.

View a streaming video of Lecture II using the free RealPlayer.

View a streaming video of Lecture III using the free RealPlayer.

Bio: Andrei Okounkov was born in 1969 in Moscow. He studied in Moscow State University from which he received his bachelor's and master's degrees as well as his doctorate in mathematics (1995). Since then he has taught at the University of Chicago and UC Berkeley, has been a member of the Institute for Advanced Study and the Mathematical Sciences Research Institute in Berkeley, has been a research fellow in the Dobrushin Mathematical Laboratory at the Institute for Problems of Information Transmission at the Russian Academy of Sciences, and is now Professor of Mathematics at Princeton University. Andrei is a recipient of the Sloan Research Fellowship (2000), a Packard Fellowship (2001), the European Mathematical Society Prize (2004), and the Fields Medal (2006). His research interests are in representation theory and its application to algebraic geometry, mathematical physics, probability, and special functions.