Geometric Invariant Theory

Abstract:

Quotients are naturally arising objects in mathematics. They allow us to study "smaller" objects and remove unnecessary data, by considering equivalent elements as the same. Often we may wish to take a quotient of a geometric object and preserve some sort of geometric structure on the quotient object. In this talk, I will explain the construction of quotients of affine and projective varieties by reductive groups, and mention some recent results regarding how differently constructed quotients are related.