Xudong Zheng : The geometry of Hilbert scheme of points on surfaces

Posted by Jeremy Kun , part of the Graduate Student Colloquium.

At

Sept. 21, 2015, 4 p.m.

In

BH 209

Abstract

One of the central endeavor in algebraic geometry is to understand geometric objects in families, hence the study of moduli spaces. These are parameter spaces where each point corresponds to an object of some kind. I will focus on one particular such moduli space, the Hilbert scheme of points. The first part of the talk will concentrate on its local geometric properties. Later I will put more emphasis on several of its applications in enumerative geometry, representation theory, and combinatorics. By the end I will mention some current research on the Hilbert scheme of points. There will be food.