Systolic S1-index and Characterization of Non-smooth Zoll Convex Bodies

Join this mathematical lecture where Stefan Matijević from Ruhr-Universität Bochum explores the systolic S1-index of convex bodies and its applications in symplectic geometry. Learn how this index serves as a symplectic invariant and how it can be used to define generalized Zoll convex bodies. Discover the equivalence between this new definition and traditional characterizations in smooth settings, along with how generalized Zoll convex bodies can be characterized using Gutt–Hutchings capacities. The presentation also demonstrates that the space of generalized Zoll convex bodies is closed within the space of all convex bodies, leading to the important conclusion that if a convex body's interior is symplectomorphic to a ball's interior, it must be generalized Zoll (and specifically Zoll if its boundary is smooth). This talk is part of the Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar series scheduled for April 11, 2025.