Wednesday, April 19, 2023
04/19/2023 - 1:00pm
We present a new method to solve the scattering problem defined by two planar, rectangular, semi-infinite open wave guides that meet along a common perpendicular line. We use the method of fundamental solutions to reduce the scattering problem to a system of Fredholm integral equations along a line. This method lends itself to numerical implementation.
04/19/2023 - 4:15pm
Given a submanifold of Euclidean space, Colding and Minicozzi defined its entropy to be the supremum of the Gaussian weighted surface areas of all of its translations and dilations. While initially introduced to study singularities of mean curvature flow, it has proven to be an interesting geometric measure of complexity. In this talk I will survey some of the recent progress made on studying the Colding-Minicozzi entropy of hypersurfaces. In particular, I will discuss a series of work by Lu Wang and myself showing closed hypersurfaces with small entropy are simple in various senses.