Due to the COVID-19 pandemic the seminars are postponed to October 2020.

Abstract: We study the positive principal eigenvalue of a weighted problem as- sociated with the Neumann Laplacian. This analysis is related to the inve- stigation of the survival threshold in population dynamics. When trying to minimize such eigenvalue with respect to the weight, one is lead to con- sider a shape optimization problem, which is known to admit spherical optimal shapes only in very specific cases. We investigate whether sphe- rical shapes can be recovered in general situations, in some singular per- turbation limit. These are joint works with Dario Mazzoleni (Universita` Cattolica del Sacro Cuore) and Gianmaria Verzini (Politecnico di Milano).