Explore a 54-minute lecture on the Hofer-Zehnder conjecture from 1992 concerning periodic points of Hamiltonian diffeomorphisms. Delve into recent advancements towards proving this conjecture, examining the utilization of persistence modules and their barcodes, as well as power operations in Floer cohomology. Gain insights into this complex mathematical topic presented by Egor Shelukhin at the ICBS2024 conference, hosted by BIMSA.