MetHods in Mixed Characteristic Geometry

The purpose of the school is to bring together people interested in learning about methods which lead to the recent progress in birational geometry and commutative algebra in mixed characteristic. Exciting developments in recent years include the successful development of the three dimensional MMP in mixed characteristic (0, p > 5), following the resolution of the long-open Direct Summand Conjecture and proof of the Cohen-Macaulayness of absolute integral closures. The school will feature two multi-lecture series by leading experts complemented by interactive exercise sessions that reinforce and expand upon the material covered, as well as a selection of invited talks by scholars working in related areas.

Organized by: Manuel Blickle (JGU Mainz) | Karl Schwede (U Utah) | Kevin Tucker (UIC)

Lecture Series

Linquan Ma (Purdue)/Hanlin Cai (Columbia)/Kevin Tucker (UIC): Prismatic cohomology and applications to commutative algebra

Abstract: We give an introduction to prismatic cohomology. We will focus on its connections to perfectoid rings, the almost purity theorem, and its applications to mixed characteristic commutative algebra via the perfectoidization functor.

Jakub Witaszek (Princeton): Riemann-Hilbert correspondence and applications to singularities

Abstract: We will provide a brief introduction to the theory of perverse sheaves as well as Riemann-Hilbert correspondences in positive and mixed characteristics. We will focus on applications to commutative algebra, particularly to the theory of splinters.

ExeRcise Sessions

There will be daily exercises sessions accompanying the lecture series. Theses are lead by:

Hanlin Cai (Utah), Rankeya Datta (Missouri), Eamon Quinlan-Gallego (Utah), and Devlin Mallory (BCAM).

Invited Talks

Fabio Bernasconi (Sapienza University of Rome): The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails

Walter Gubler (Regensburg): On the non-archimedean Monge-Ampère equation in mixed characteristic

Arthur-César Le Bras (CNRS): de Rham Fargues-Fontaine stacks

Wiesława Nizioł (CNRS): Hidden structures on de Rham cohomology of p-adic analytic varieties

Charles Vial (Bielefeld): On proper splinters in positive characteristic

Registration and financial support

There is a limited amount of financial support for local expenses available for graduate students and postdocs. In order to be considered for first round of funding fill out the registration form by June 10th 2024.