Mean width, symplectic capacities and volume

Abstract: In this talk, I will discuss an inequality between a symplectic version of the mean width of a convex body and its symplectic capacity. This is motivated by and generalizes an equality established by Artstein-Avidan and Ostrover. The proof utilizes their symplectic Brunn-Minkowski inequality together with a local version of Viterbo's conjecture established by Abbondandolo and Benedetti. I will also describe several examples and secondary results that suggest that the difference between the symplectic mean width and the mean width is deeply related to toric symmetry. This is joint work in progress with Jonghyeon Ahn.

differential geometrydynamical systemsgeometric topologysymplectic geometryspectral theory

Audience: researchers in the topic

Geometry and Dynamics seminar

Series comments: On the week of the seminar, an announcement with the Zoom link is mailed to the seminar mailing list. To receive these e-mails, please sign up by writing to Lev Buhovsky (http://www.math.tau.ac.il/~levbuh/).