Title: Moduli spaces, deformation theory, and noncommutative varieties
Abstract: In algebraic geometry, a moduli space is a space that parametrizes a class of objects, with each object represented by a point in the moduli space.
Deformation theory is the study of the neighborhood of a point of the moduli space. For example, the deformation theory of an algebraic variety classifies which varieties are "near" a given algebraic variety in the moduli space.
In this talk, I will discuss some examples of things you can learn from basic deformation theory. I will also discuss some recent results in this area which use the tools of modern algebraic geometry to deform an algebraic variety in a noncommutative direction.