Our colloquium takes place on the first Tuesday of each month from 15:30 to 16:30, usually in room A709.
A renowned expert (being an excellent speaker as well) visits us for an afternoon and gives a panorama of one of her research areas. The talk is meant to be accessible to all members of the lab, including PhD students in analysis, game theory, probability and statistics. Ideally, it should start gently with an historical background on the problem and an overview of the main questions and applications, keeping a non technical style during at least the first half of the talk. Of course it is also nice to have a part with more mathematical details: the most appreciated colloquia were those in which the speaker succeeded to develop a nice technical idea or an elegant argument that everyone should know.
Food and drinks are served after the event, usually in Espace 7!
Date: Tuesday, May 6th 2025 (15:30-16:30, room A709)
Speaker: (Ludwig Maximilians Universität München)
Title: Sharp functional inequalities and their stability
Abstract: The Sobolev inequality is a paradigmatic example of a functional inequality with many applications in the Calculus of Variations, Geometric Analysis and PDEs. In some of these applications the optimal value of the constant is of importance, as is a characterization of the set of optimizers. The stability question is whether functions whose Sobolev quotient is almost minimal are close to minimizers of the inequality and, if so, in which sense. We give a gentle introduction to this question and review some recent results on the Sobolev inequality and other functional inequalities of a similar nature.