Emil Grosswald Lectures 2010

Andrei Okounkov, Princeton University

From the longest increasing subsequence to instanton counting

A series of three talks on topics related to the Plancherel measure

Abstract:

Random partitions pop up in many areas of mathematics, sometimes directly but more often in disguise. There are some very natural probability measures on partitions, such as the Plancherel measure, whose behavior we understand very well thanks to the rich algebraic structure that the partitions possess. The Plancherel measure underpins the classical Ulam problem about the longest increasing subsequence in a random permutation and plays a key role in Nekrasov's theory of instanton counting. The aim of my lectures will be to explain what is the Plancherel measure, how did we learn what we know about it, and which conclusions can we draw from this for various applications.

Tuesday April 20, 4:00 PM: Andrei Okounkov, Princeton University, Lecture 1.
Wednesday April 21, 4:00 PM: Andrei Okounkov, Princeton University, Lecture 2.
Thursday April 22, 4:00 PM: Andrei Okounkov, Princeton University, Lecture 3.

Tea will be served before the lectures at 3:30pm, in the mathematics lounge next to the conference room. All the talks will take place in room 617 of Wachman Hall on the main campus of Temple University in Philadelphia, Pennsylvania.