## Number Theory Seminar

### Wednesday, July 4th, 2018

**Time:** 2:30-3:20p.m. **Place:** Jeffery Hall 422

**Speaker:** Siddhi Pathak (Queen's University)

**Title:** THE SELBERG TRACE FORMULA.

**Abstract:** Let $G$ be a locally compact group and $\Gamma$ be a discrete subgroup of $G$ such that $\Gamma \backslash G$ is compact. In 1956, A. Selberg introduced the trace formula relating the traces of irreducible unitary representations of G on $L^2(\Gamma \backslash G)$ to orbital integrals.

In this talk, we will give a brief exposition on Tamagawa's formulation of the Selberg trace formula. Further, we will emphasize that the Poisson summation formula as well as the Frobenius reciprocity for finite groups are special cases of the Selberg trace formula.