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\textbf{SPEAKER}:
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%\textbf{SPEAKER}:
 Kiril Datchev, Purdue University
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{\bf TITLE}:
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Low energy scattering asymptotics in dimension two
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{\bf ABSTRACT:}\\
Analysis of the Laplacian at low energy involves special
challenges in dimension two. I will present a new technique, which is
elementary and robust, for scattering theory in this setting, focusing on
the fundamental example of obstacle scattering. The technique is based on a
resolvent identity of Vodev. By an identity of Petkov and Zworski we deduce
expansions for the scattering matrix and scattering phase, and similarly
obtain expansions for the exterior Dirichlet-to-Neumann operator.

The leading singularities at low energy are given in terms of the obstacle's
logarithmic capacity or Robin constant.  We expect these results to hold for
more general compactly supported perturbations of the planar Laplacian, with
the definition of the Robin constant suitably modified, under a generic
assumption that the spectrum is regular at zero. This talk is based on joint
work with Tanya Christiansen.





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