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Geometry, Symmetry and Physics Seminar

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

Y. Baris Kartal (Princeton)

Location:  Contact organizers for link
Date & time: Thursday, 11 June 2020 at 2:00PM - 3:00PM

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.