Geometry working seminar

Talk 1. Ehsaan Hossain, Pure Mathematics Department, University of Waterloo

“Divisors on an algebraic curve”

So far we’ve seen Pic(X) as the set of (isomorphism classes of) line bundles on X. When equipped with tensor product it becomes an abelian group, which turns out to be equivalent to the group H1(OX∗). This is true for any ringed space (X,OX). In this presentation we’ll see a third interpretation: if X is a smooth algebraic curve then Pic(X) can be described by divisors.

Talk 2. Mohamed El Alami, Pure Mathematics Department, University of Waterloo

“First-order deformations”

The object of this talk is to introduce deformation theory and the moduli problem. Our focus will be on deformations of differentiable structures. If time permits, we will also talk about deformations of algebraic structures.