### Representations of p-adic groups

Heilbronn Number Theory Seminar

27th March 2019, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

In the 1990s Moy and Prasad revolutionized the representation theory of p-adic groups by showing how to use Bruhat-Tits theory to assign invariants to representations of p-adic groups. The tools they introduced resulted in rapid advancements in both representation theory and harmonic analysis -- areas of central importance in the Langlands program. A crucial ingredient for many results is an explicit construction of (types for) representations of p-adic groups. In this talk I will indicate why, survey what constructions are known (no knowledge about p-adic groups assumed) and present recent developments based on a refinement of Moy and Prasad's invariants.

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