Smith Theory in Floer Persistence and Dynamics

This lecture by Egor Shelukhin, partially with Jingyu Zhao, covers Smith theory in Floer persistence and dynamics, starting with a biased view of invariants in classical mechanics, leading to the Poincaré-Birkhoff theorem and Arnol'd's reformulation. The homological Arnold conjecture and the Hofer-Zehnder conjecture are discussed, along with the main results and interpretations. The lecture delves into the Smith theory in filtered symplectic Floer homology, exploring theorems and corollaries related to pseudo-rotations and quantum homology. The presentation concludes with an outline of the proof of the main theorem and the idea of using p-legged pants with symmetric Floer data in Smith theory.