Speaker: Dr. Bingyu Zhang (University of Southern Denmark)
Time: 10:30-11:30  July 21st, 2025 (Monday)
Venue: MCM110

Title: Novikov ring from microlocal sheaves

Abstract: In this talk, I explain how to relate the Novikov ring and microlocal sheaf theory based on the works of Tamarkin and Vaintrob, and its higher dimension version as a mirror symmetry type result. This relation has been successfully applied to irregular Riemann-Hilbert correspondence and symplectic geometry, and recently, Scholze revealed certain potential applications of the relation in analytic geometry. Surprisely, 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. In particular, certain almost purity phenomena appear in the structure of the Fukaya category over the Novikov ring, with potential applications in homological mirror symmetry over the Novikov ring.