Towards the HZ- and Multiplicity Conjectures for Dynamically Convex Reeb Flows

Join this advanced mathematics lecture where Basak Gurel from the University of Central Florida explores the multiplicity question for prime closed orbits of dynamically convex Reeb flows on the boundary of 2n-dimensional star-shaped domains. Learn about two significant results: first, the proof that such flows have at least n prime closed Reeb orbits, confirming Ekeland's conjecture; and second, that when the domain is centrally symmetric with non-degenerate Reeb flow, there exist either exactly n or infinitely many prime closed orbits. Discover how this second theorem represents a higher-dimensional contact variant of Franks' 2-or-infinity theorem and addresses a specific case of the contact Hofer-Zehnder conjecture. The presentation is based on joint work with Erman Cineli and Viktor Ginzburg as part of the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar series.