Talk 1. Ritvik Ramkumar - 1:00pm
Pure Mathematics Department, University of Waterloo
“An introduction to complex analysis in several variables”
I will start by going over some basic results from complex analysis in one variable. Using these results I will deduce some important theorems in multi-variable complex analysis such as the Weierstrass preparation theorem and give some applications. I will also introduce the notion of an analytic variety and describe some of their interesting properties.
Talk 2. Ehsaan Hossain - 2:30pm
Pure Mathematics Department, University of Waterloo
“Vector bundles and sheaves”
We will introduce the notion topological/smooth/holomorphic vector bundle, and present some basic examples and constructions. Vector bundles are related to sheaves via their sections, and also have counterparts in commutative algebra. Time permitting, we will explain how vector bundles correspond to locally free sheaves of modules.