Jessica Fintzen: An introduction to representations of p-adic groups

Talk at the "Mathematics Münster Mid-term Conference", 25-27 March 2024, in Münster, Germany.
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, but also for the construction of an explicit and a cate- gorical local Langlands correspondence, and has applications to the study of automorphic forms, for example.
In my talk I will introduce p-adic groups and explain that 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 Jeffrey Adler, Manish Mishra and Kazuma Ohara to reduce a lot of problems about the (category of) representations of p-adic groups to problems about representations of finite groups of Lie type, where answers are often already known or easier to achieve.
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