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# CRC-Colloquium

## January 25 at 17:00 – 18:00 CET

15:30 Uhr Ben Heuer (Universität Frankfurt): p-adic non-abelian Hodge theory for non-p-adic mathematicians

16:30 Coffee and Cake

17:00 Uhr Jan Bruinier (TU Darmstadt): Theta functions in geometry and arithmetic

18:30 Uhr: Dinner

Abstract B. Heuer:

In p-adic non-abelian Hodge theory, we study p-adic representations of fundamental groups of projective varieties. This talk will give an introduction to this subject without assuming any background in p-adic geometry. Based on examples, I will explain the “p-adic Simpson correspondence”, with an emphasis on the relation to complex geometry. I will discuss recent advances, the main open questions in the area, and potential applications to complex geometry.

Abstract J. Brunier:

We explain how theta functions can be used to study positive definite quadratic forms and their representation numbers. For indefinite quadratic forms, Kudla and Millson showed that there are analogous theta functions relating the geometry of special cycles on locally symmetric spaces to modular forms. Conjectures of Kudla predict similar results for arithmetic special cycles in Arakelov Chow groups on integral models of orthogonal Shimura varieties. We will also report on some recent results in this context.

Zoom Meeting-ID: 967 5163 9626

Passcode: last name of famous mathematician born in Königsberg (small letters)