Speaker: Tanya Christiansen (University of Missouri)

Title: Resonances in even-dimensional Euclidean scattering

Abstract: Resonances may serve as a replacement for discrete spectral data for a class of operators with continuous spectrum. In odd-dimensional Euclidean scattering, the resonances lie on the complex plane, while in even dimensions they lie on the logarithmic cover of the complex plane. In even-dimensional Euclidean scattering there are some surprises for those who are more familiar with the odd-dimensional case. For example, qualitative bounds on the number of “pure imaginary” resonances are very different depending on the parity. Moreover, for Dirichlet or Neumann obstacle scattering or for scattering by a fixed-sign potential one can show there are many resonances in even dimensions. In fact, for these cases the $m$th resonance counting function ($m\in Z, m\neq 0$) has maximal order of growth.