Room P3.10, Mathematics Building

Richard Laugesen, University of Illinois at Urbana-Champaign
Spectrum of the Robin Laplacian: recent results, and open problems

I will discuss two recent theorems and one recent conjecture about maximizing or minimizing the first three eigenvalues of the Robin Laplacian of a simply connected planar domain. Conformal mappings and winding numbers play a key role in the geometric constructions. In physical terms, these eigenvalues represent decay rates for heat flow assuming a “partially insulating” boundary.

Joint with the CEAFEL seminar

Projecto FCT UID/MAT/04459/2019.