Vendredi 2 octobre 2020 à 10h30, exposé en ligne sur BBB :
Yuichi Ike (Fujitsu Lab)
Persistence-like distance on Tamarkin category and displacement energy
Abstract: In this talk, I will talk about relation among the microlocal theory of sheaves, persistence modules, and symplectic geometry.
The microlocal theory of sheaves due to Kashiwara and Schapira can be regarded as Morse theory with sheaf coefficients.
Recently it has been applied to symplectic geometry, after the pioneering work of Tamarkin. We introduce a persistence-like
distance on Tamarkin sheaf category and prove a stability result with respect to Hamiltonian deformation of sheaves.
Using this result, we propose a sheaf-theoretic method to give a lower bound of the displacement energy of compact subsets
of a cotangent bundle. If time permits, I also explain our recent result on intersection of rational Lagrangian immersions
based on the sheaf-theoretic method. This is a joint work with Tomohiro Asano.