2024 Program for Women+ and Mathematics
Colloquium: An Introduction to Representations of p-adic Groups
Abstract: An explicit understanding of the category of all (smooth, complex) representations of p-adic groups provides an important tool not just within representation theory. It also has applications to number theory and other areas, and in particular enables progress on various very different forms of the Langlands program (the topic of the Uhlenbeck lectures).
In this talk, I will introduce p-adic groups and explain how the category of representations of p-adic groups decomposes into subcategories, called Bernstein blocks. I will then provide an overview of what we know about the structure of these Bernstein blocks. In particular, I will sketch how to use a joint project in progress with Adler, Mishra and Ohara to reduce a lot of problems about the representations of p-adic groups to problems about representations of finite groups of Lie type (compare the Terng lectures), where answers are often already known or are at least easier to achieve.