数学科学学院短期课程

Almost mathematics in log-perfectoid toric mirror symmetry

张秉宇

（南丹麦大学）

时间：2025.11.04-11.18  14:00—15:00（每周二下午）

地点：腾讯会议：686-9079-9616（密码：1024）

摘要：In these lectures, I will explain a version of toric mirror symmetry equivalence proposed by D. Vaintrob that relates the category of all topological sheaves and the category of almost quasi-coherent sheaves on the Novikov version of toric varieties based on a work joint with Tatsuki Kuwagaki. The proof is based on the microlocal theory of topological sheaves, but we realized amazingly that the role of almost mathematics, originally invented for p-adic Hodge theory, is essential. The 1-dimensional case of the correspondence already has fruitful applications, especially in (quantitative) symplectic geometry, algebraic K-theory, and irregular Riemann-Hilbert correspondence; on the other hand, potential applications for arithmetic geometry have been proposed by Peter Scholze under the name wild Betti sheaves.

There will be 3 lectures on the following contents: 1) Basic microlocal sheaf theory. 2) Proof for the 1-dimensional and its applications. 3) Proof for higher dimension cases.

授课人简介：Bingyu Zhang is currently a postdoc at Center for quantum mathematics on University of Southern Denmark. His research focuses on microlocal sheaf theory, and related symplectic geometry and algebraic K-theory.

邀请人：张旭成

欢迎大家参加！