|Date: Friday, February 16, 2018
Location: 3096 East Hall (3:10 PM to 4:00 PM)
Title: An introduction to deformation theory
Abstract: Deformation theory can be thought of as the infinitesimal study of global families, and provides a powerful tool for study of moduli and degenerations. It's also a subject rich with explicit calculations, which demonstrate the practical utility of notions such as sheaf cohomology, flatness, nilpotents, and the functor of points. In this talk, we'll give an introduction to the basics of deformation theory, focusing on the first-order deformations of several types of objects (subschemes, line bundles, coherent sheaves, and abstract schemes). In particular, we'll give several applications to the infinitesimal study of the Hilb and Pic schemes, obtain a heuristic estimate for the dimension of the moduli space of genus g curves, and study the relation between different types of deformations. Time permitting, we'll also sketch a striking application, due to Mori, which uses deformation theory along with the frobenius to produce rational curves on certain varieties. The talk will focus on explicit examples and computations, and should be accessible to students who've taken 631, although a little knowledge of sheaf cohomology may be useful.
Speaker: Devlin Mallory