Presenter: Charlotte Chan, Michigan, USA

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.

### About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 3pm to 3.50pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

#### Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

#### Contact us

To volunteer to talk or to suggest a speaker, email Ole Warnaar or Travis Scrimshaw.