PDE Seminar Abstracts

Topology, Index Theory, and Scattering on Surfaces With Euclidean Ends

Leo Tzou
University of Sydney, Australia
Monday12 October 2015, 2-3pm, Carslaw Room 535A


On a surface with Euclidean ends we recover the connection (rough) Laplacian, up to isomorphism, from its scattering matrix. This problem turns out to be intimately related to the topology of the surface and we see how classical index theorems such Riemann-Roch can play a siginificant role in understanding this relationship.