### Spring 2023

### MATH GR8210 – **PARTIAL DIFFERENTIAL EQUATIONS**

**Instructor**: Panagiota Daskalopoulos

**Day/Time**: TR 11:40am-12:55pm

**Room:** 622 MATH (tentative)

**Title**: TBD

**Abstract**: TBD

### Fall 2022

### Math GR8659 – **TOPICS IN AUTOMORPHIC FORMS**

**Instructor**: Michael Harris

**Day/Time**: TR 01:10pm-02:25pm

**Room:** 622 MATH

**Title**: Hodge-Tate theory and p-adic automorphic forms

**Abstract**: Lue Pan’s recent work on the completed cohomology of modular curves, which uncovered unexpected relations between the p-adic Simpson correspondence, D-modules, and p-adic Hodge theory, points toward a direct role for representation theory in the p-adic theory of automorphic forms. Subsequent reinterpretations and generalizations in higher dimension by Pilloni and Rodríguez Camargo, represent important steps toward developing a geometric theory of p-adic automorphic forms comparable to that already known for the complex theory.

The course will focus on the work of Lue Pan and Pilloni, with the ultimate aim of making Rodríguez’s more complete but much more technically demanding article more approachable. Necessary notions from (Scholze’s) p-adic geometry and functional analysis, p-adic Hodge theory, and the localization theory of D-modules on flag varieties will be introduced as necessary. The course will aim more at clarifying ideas than at providing complete proofs.

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