Presented by: 
Charlotte Chan, Michigan, USA
Tue 15 Aug, 2:00 pm - 3:00 pm

The representation theory of SL2(Fq) can be studied via the geometry of the Drinfeld curve. This is a special case of Deligne--Lusztig theory, which gives a beautiful geometric construction of the irreducible representations of finite reductive groups. In 1979, Lusztig gave a conjectural analogue of this story for p-adic groups. We verify this conjecture in the setting of division algebras, and along the way, we prove two conjectures of Boyarchenko in full generality. We use geometric trace formulas to prove that Lusztig's construction induces a cohomological realization of the Jacquet--Langlands correspondence.