Speaker: Dr Euan Spence (University of Bath)
Title: For most frequencies, strong trapping has a weak effect in frequency-domain scattering
It is well known that when the geometry and/or coefficients allow stable trapped rays, the solution operator of the Helmholtz equation (aka the resolvent of the Laplacian) grows exponentially through a sequence of real frequencies tending to infinity.
In this talk (based on the paper For most frequencies, strong trapping has a weak effect in frequency-domain scattering) we show that, even in the presence of the strongest-possible trapping, if a set of frequencies of arbitrarily small measure is excluded, the Helmholtz solution operator grows at most polynomially as the frequency tends to infinity.
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