报告题目：Partitions, algebraic geometry and representation theory

时间：2008年7月8日（周二下午）15：00 —— 16：00

地点：中山北路校区，理科大楼 A510

主讲人：Zhenbo Qin 教授 (美国University of Missouri)

内容简介: We use the Hilbert schemes of points on complex surfaces to illustrate interplay among combinatorics, algebraic geometry and representation theory. The basic model is the Hilbert schemes of points on the complex plane, whose Euler characteristics coincides with the number of partitions. Its cohomology group follows from H. Nakajima's construction of an infinite dimensional Heisenberg algebra action. For the Hilbert schemes of points on an arbitrary complex surface, we review the main results obtained in a series of joint papers (with W.-P. Li and W. Wang) via vertex algebra techniques and their connections with works of A. Okounkov and R. Pandharipande. We end with a discussion of Y. Ruan's Cohomological Crepant Resolution Conjecture for these Hilbert schemes.