Department of

Mathematics


Seminar Calendar
for events the day of Thursday, March 26, 2020.

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Thursday, March 26, 2020

4:00 pm in 245 Altgeld Hall,Thursday, March 26, 2020

Trapping, resonances, and the decay of waves [to be rescheduled Fall 2020]

Jared Wunsch   [email] (Northwestern University)

Abstract: I will discuss some results, new and old, involving the influence of the geometry on the decay of waves. The quantum correspondence principle dictates that at high frequency, the dynamics of particle trajectories should be related to the rate at which the energy of a solution to the wave or Schrödinger equation decays. This relationship is mediated by the existence of resonances, which correspond to states with a finite (but possibly long) lifetime that ultimately decay owing to tunneling effects. I will discuss what we know about the existence and nonexistence of resonances, and focus on some recent results about resonances associated to the subtle effects of diffraction in classical and quantum problems that have singular structures in a metric or potential.