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Seminar on microlocal analysis and applications
Diffraction and Wave Trace of the Aharonov--Bohm Hamiltonian
Diffraction and Wave Trace of the Aharonov--Bohm Hamiltonian
Organizers
Xi Chen
,
Long Jin
Speaker
Mengxuan Yang
Time
Friday, November 5, 2021 10:00 AM - 11:00 AM
Venue
1129B
Abstract
Hormander's classic theorem shows that singularities of solutions to the wave equation propagate along the geodesic flow. Duistermaat--Guillemin trace formula gives leading order singularities of the wave trace on closed manifolds. In this talk, we will discuss the analogous results for wave equations with singular magnetic vector potentials, which correspond to the celebrated Aharonov--Bohm effect. A result on a lower bound of the number of resonances will also be discussed.