Stratified bundles, p-adic differential equations and spectral theory

Thời gian: 16h30, thứ 5 ngày 2/2/2023

Địa điểm: Phòng 612 nhà A6, Viện Toán học

Link online: https://meet.google.com/yep-kbzk-eao?pli=1&authuser=4

Tóm tắt: In this series of talks (with T. Bao), we will review the notion of "regularity" of D-modules in the p-adic setting. To do so, we first recall some kinds of rings (and their properties) that frequently occur in the p-adic world: Robba ring, Witt ring, Cohen ring, and analytic ring, etc. By considering the relation between Robba ring and analytic ring, some questions related to the paper of Matzat-v.d.Put (Iterative differential equations and the Abhyankar conjecture) will be raised and discussed. In the second part, we will introduce the spectral theory of differential operators (Kedlaya's works). This will particularly allow us to see the similarity between two classical notions in this field: Poincare-Katz rank and p-adic convergent radii of solutions in Berkovich geometry. In the end, we introduce a "spectral" criterion of the existence of Turrittin-Levelt decomposition of irregular formal connections over a DVR.