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Computations of eigenvalues and resonances on non-compact manifolds with regular ends: from water waves to number theory

Colloquium

Computations of eigenvalues and resonances on non-compact manifolds with regular ends: from water waves to number theory
Series: Colloquium
Location: MATH 501
Presenter: Michael Levitin, University of Reading

"In the first part of the talk I’ll give an overview of a simple method which allows to compute eigenvalues and resonances (of a Laplace or a Shroedinger operator) on non-compact manifolds with regular ends (that is, such that variables separate at infinity) using the so-called Dirichlet-to-Neumann map. In the second part, I will discuss a recent paper (joint with Alex Strohmaier) where these techniques are applied to perturbed hyperbolic surfaces with cusps — thus allowing us to do some Number Theory using Finite Element Method.

The talk will be elementary — no prior knowledge of either hyperbolic geometry, number theory or numerical analysis will be required.”