Dr. Christian Klevdal (University of California San Diego)

10/21/2024  4:10pm

Abstract: 

In an undergraduate mathematics curriculum, most courses could reasonably be placed into one of the following topics: algebra, geometry or analysis. In reality, though, this categorization is not so clear as many subjects involve a mixture of two or all three of these topics, and oftentimes the interplay between these topics lead to very interesting results! 

 
The goal of this talk is to discuss how one important area of modern number theory, the Langlands program, can be seen as a bridge between algebra, geometry, and analysis. We will start with one of the most astounding results in number theory: Wiles' proof of Fermat's last theorem, where the key insight was a connection between elliptic curves (geometry), modular forms (analysis), and Galois representations (algebra). We will then discuss how certain geometric objects facilitate this connection.