Back to Departmental Colloquium: Spring 2021
Departmental Colloquium
Date: Tuesday, Jan 26, 2021
Time: 4:00PM
Location: JWB 335
Harold Blum
Stony Brook University
Title |
Moduli spaces of Fano varieties and K-stability |
Abstract |
Algebraic geometry is focused on the study of algebraic varieties, which are shapes cut out by polynomial equations. A fundamental problem in the field is to construct and study spaces that parametrize algebraic varieties of a given type, referred to as moduli spaces. The quintessential example of such a parameter space is the moduli space of curves, which is a space whose points are in bijection with isomorphism classes of Riemann surfaces. After surveying these ideas, I will discuss the problem of constructing moduli spaces parametrizing Fano varieties, which are a class of complex manifolds that form one of the three main building blocks of varieties in algebraic geometry. A new approach to this problem relies on the notion of K-stability, which is an algebraic definition introduced by differential geometers to characterize when a Fano variety admits a certain canonical metric. |
Algebraic Geometry
Topology
Geometry and Topology