David Sher (DePaul University)

Title: The Dirichlet heat trace for domains with curved corners

Abstract: Consider the heat problem with Dirichlet boundary conditions on a curvilinear polygon in the plane. We examine the short-time asymptotic expansion of the associated heat trace, focusing on the interaction between the curvature of the boundary and the corners of the domain. The coefficients of this expansion are well-understood in the case where the curvilinear polygon has ``straight corners", that is, where each corner is locally isometric to the tip of a Euclidean sector. In the setting where the curvature is nontrivial all the way down to a corner, much less is known. In this talk, I will explain why the interaction of the curvature and corner does contribute to the heat trace expansion, characterize the form of this contribution, and compute it explicitly in a special case. This is joint work with Sam Looi (Caltech).

Hybrid seminar at UdeM, Pavillon André-Aisenstadt, room 5183

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