The HADES seminar on Tuesday, September 20th will be at 3:30 pm in Room 740.

Speaker: Moritz Doll

Abstract: On a scattering manifold, we consider a Schrödinger operator of the form
$H = -\Delta + V(x)$, where the potential satisfies a growth condition that
generalizes quadratic growth for Euclidean space. These types of
operators were first investigated by Wunsch, who proved a relationship
between singularities of the wave trace and a Hamiltonian flow. On the
other hand, it is easy to see that the heat trace is smooth away from
$t=0$ and our goal is to calculate the asymptotic expansion of the heat
trace as $t \to 0$. We follow the approach of Melrose by constructing a
suitable space on which the integral kernel of the heat operator is
smooth and then using the push-forward theorem to calculate the heat
trace asymptotics. This is based on ongoing joint work with Daniel Grieser.