Novikov ring from microlocal sheaves

In this talk, I will explain how to relate the Novikov ring and microlocal sheaf theory based on the works of Tamarkin and Vaintrob. This relation has been successfully applied to the irregular Riemann-Hilbert correspondence and symplectic geometry, and recently, Scholze revealed certain potential applications of the relation in analytic geometry. Surprisingly, we notice that the almost ring theory invented by Faltings for p-adic Hodge theory plays a central role in the related construction. After that, I will explain some applications of the idea in symplectic geometry.

This talk is based on a joint work with Tatsuki Kuwagaki.