Almut Burchard (University of Toronto)

Title: Symmetry-breaking in geometric capacitor problems.

Abstract: How does the shape of a body determine its capacity? Classical results say that balls _minimize_ the Newton capacity among bodies of given volume, but _maximize_ it among bodies of given diameter. While  the lower bound on capacity in  terms of volume is a cornerstone  of potential theory,  the upper bound in terms of diameter (proved by Szego in 1930) was largely relegated to a footnote. Recently isodiametric shape optimization for Riesz capacities has become interesting in the context of aggregation problems with pair interactions  of attractive-repulsive type. In this talk I will discuss situations where the capacity-maximizer is not a ball. When does symmetry-breaking occur, and what are good candidates for non-radial maximizers?

Location: Hybride - CRM, Salle / Room 6214, Pavillon André Aisenstadt