Generalized Convex Toric Domains and Symplectic Embedding Problems

Explore advanced symplectic geometry through this mathematical lecture examining generalized convex toric domains and their applications to symplectic embedding problems. Delve into the geometric properties of 4-dimensional convex toric domains defined as preimages of bounded convex regions under moment maps, focusing on how boundary curvature and affine perimeter influence symplectic packing problems. Investigate the asymptotic behavior of ECH (Embedded Contact Homology) capacities, which follow a Weyl law and detect volume properties, while discovering how their subleading asymptotics reveal information about affine perimeter. Learn how these asymptotic results generate new insights and applications for solving symplectic embedding problems, with research findings based on collaborative work with Dan Cristofaro-Gardiner and Dusa McDuff. This presentation is part of the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar series, delivered by Nicki Magill from the University of California, Berkeley.