### 27 november 2008, kl 13.15-14.15, Uppsala universitet, Ångström,
sal 64119.

###
Henrik Ueberschaer (University of Bristol):
The trace formula for singular perturbations of the Laplacian on a
hyperbolic surface

**Abstract.**
Hyperbolic surfaces of finite volume are objects of study in Quantum Chaos
since the geodesic flow on such surfaces is known to be ergodic. Selberg's trace
formula famously links the eigenvalues of the Laplacian on such a surface to geometric
quantities such as periodic orbits.
I will present an analogue of Selberg's trace formula for a delta
potential on a hyperbolic surface. In the case of a non-compact surface
with a single cusp I will present perturbative analogues of classical
Maass forms and nonholomorphic Eisenstein series which naturally arise in
the development of the trace formula.