Almut Burchard (University of Toronto)
罢颈迟濒别:听Symmetry-breaking in geometric capacitor problems.
础产蝉迟谤补肠迟:听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 聽the lower bound on capacity in 聽terms of volume is a cornerstone 聽of potential theory, 聽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 聽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?
尝辞肠补迟颈辞苍:听Hybride - CRM, Salle / Room 6214, Pavillon Andr茅 Aisenstadt