p-adic analytic actions on Fukaya categories and iterations of symplectomorphisms

Abstract: Inspired by the work of Bell on dynamical Mordell-Lang conjecture and by family Floer homology, we construct p-adic analytic actions on the Fukaya category of a non-degenerate, monotone symplectic manifold satisfying some assumptions. Using this, we deduce results on the change of rank of Lagrangian Floer homology groups $HF(\phi^k(L),L')$ as $k$ varies, for a symplectomorphism $\phi$ isotopic to identity.

Mathematics

Audience: researchers in the topic

Rutgers symplectic geometry seminar

Series comments: Please contact the organizers for zoom link Soham Chanda, Yuhan Sun, Chris Woodward