Seminar| Institute of Mathematical Sciences
Time:Thursday, July 10th, 2025,14:00-15:00
Location:IMS, RS408
Speaker: Bingyu Zhang, University of Southern Denmark
Abstract: In this talk, I 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 irregular Riemann-Hilbert correspondence and symplectic geometry, and recently, Scholze revealed certain potential applications of the relation in analytic geometry. Supereisely, 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.