Title: What is an automorphic representation? Abstract: Andrew Wiles' famous proof of Fermat's last theorem was crucially based on constructing a mysterious connection between two classes of mathematical objects: "modular forms" and "elliptic curves". However, if you try looking up what a modular form actually is, you'll find an elementary but very unmotivated definition involving functions on […]
A Brief Introduction to Gödel's Incompleteness Theorems In 1931 Kurt Gödel proved a pair of landmark results that limited the strength of formal theories of mathematics. These "incompleteness theorems" are central to modern understandings of logic, and also to numerous misunderstandings. So today, we'll explore these theorems - how they work, how they were developed […]
Title: A Geometric Introduction to Representation TheoryAbstract: What exactly does it mean for a group to represent the symmetries of an object? In this talk, I will attempt to answer this question by convincing you that the study of group actions, or representations, comes up even more naturally than the study of groups themselves. We […]