Some Differential Operators on the Modular Curves with Infinite Level at P and Applications

Explore differential operators on modular curves with infinite level at p and their applications in this lecture by Lue Pan from Princeton University. Delivered as part of the 2021 Fields Medal Symposium honoring Peter Scholze, delve into topics such as hot state representation, notation, analogs, structure sheaths, localisation, and isomorphisms. Gain insights into the mathematical concepts and their implications in the field of algebraic geometry and number theory.

Introduction
Applications
Remarks
Hot state representation
Hot state 0k
Notation
Analogs
Structure sheath
Localisation
Hot State
Isomorphism