Joint IAS/Princeton Arithmetic Geometry Seminar

The analytic de Rham stack is a new construction in Analytic Geometry whose theory of quasi-coherent sheaves encodes a notion of p-adic D-modules. It has the virtue that can be defined even under lack of differentials (eg. for perfectoid spaces or...

Topology of the Hitchin system has been studied for decades, and interesting connections were found to orbital integrals, non-abelian Hodge theory, mirror symmetry etc. I will explain that a large part of the symmetries in these geometries above are...

I will describe the main ideas that go into the proof of the (unramified, global) geometric Langlands conjecture. All of this work is joint with Gaitsgory and some parts are joint with Arinkin, Beraldo, Chen, Faergeman, Lin, and Rozenblyum. I will...

p-adic heights have been a rich source of explicit functions vanishing on rational points on a curve. In this talk, we will outline a new construction of canonical p-adic heights on abelian varieties from p-adic adelic metrics, using p-adic Arakelov...

In this talk I want to explain some surprising features of the pro-etale cohomology of rigid-analytic varieties, and how they can be explained by a six functor formalism with values in solid quasi-coherent sheaves on the Fargues-Fontaine curve.

This...