IU-Purdue Joint Workshop on Prismatic F-gauges

April 25th – April 26th, 2026
Purdue University, Indianapolis Campus
Organizers: Daniel Le, Tong Liu, Shubhodip Mondal, and Matthias Strauch

Workshop Venue

Engineering Technology Building ET 202, Purdue University, Indianapolis Campus
799 W Michigan St, Indianapolis, IN 46202

Speakers

George N Diaz-WahlPurdue University
Zachary GardnerBoston College
Tong LiuPurdue University
Shubhodip MondalPurdue University
Mansimar SinghPurdue University
Gleb TerentiukUniversity of Michigan
Zichuan WangIndiana University
Yuanning ZhangNorthwestern University

Schedule

Saturday, April 25

TimeEvent / Speaker
10:00 AM – 11:00 AM Shubhodip Mondal
Dieudonne theory and prismatic F-gaueges We will give an introduction to Dieudonne theory and explain how a stack theoretic approach leads to general classification theorems.
11:30 AM – 12:30 PM Zachary Gardner
Apertures and the inverse syntomic Dieudonne functor

In recent work, K. Madapusi and I show that the $p$-adic formal moduli of apertures (which are certain vector bundle prismatic F-gauges) agrees with the moduli of p-divisible groups. A key part of this story is the behavior of the inverse syntomic Dieudonne functor, which follows from good control of the stacks of sections of apertures. In this talk, I want to highlight the interesting and important features of this structural analysis, notably including the Grothendieck-Messing theory of apertures and the role played by so-called Hoobler stacks. In the process, I hope to shed new light on classical aspects of Dieudonne theory.
Lunch Break
2:00 PM – 3:00 PM Yuanning Zhang
From F-crystals to Hodge-Witt cohomology

Let k be a perfect field of characteristic p. For a Mazur-Ogus variety X/k, the F-crystal structure on crystalline cohomology determines the slope filtration, which in turn controls the Hodge-Witt cohomology of X. In practice, however, making this relation explicit requires an understanding of the dominoes that govern nonvanishing differentials and unipotent phenomena in de Rham-Witt cohomology. In this talk, I will discuss a structural study of higher-dimensional dominoes and explain how it leads to explicit computations and new examples in de Rham-Witt cohomology of abelian varieties.
3:30 PM – 4:00 PM George N Diaz-Wahl
Prismatization of imperfect fieldsWe sketch a proof of an equivalence of categories between quasi-coherent sheaves on the prismatization of an imperfect field and modules over the Cohen ring with quasi-nilpotent integrable connection. We also speculate how this may generalize results of Terentiuk, Vologodsky, and Xu on Fontaine-Lafaille theory and prismatic F-gauges.
4:15 PM – 4:45 PM Mansimar Singh
Nonadmissible irreducible smooth mod p representations of p-adic reductive groupsIt is known by work of Barthel—Livne, Breuil, and Berger that every irreducible smooth mod p representation of GL_2(Q_p) is admissible. We will describe a construction of non-admissible irreducible smooth mod p representations of GL_2(F) for non-archimedean local fields F \neq Q_p using cosheaves on the Bruhat—Tits tree following ideas of Breuil and Paskunas.
5:00 PM – 5:45 PMCareer Panel

Sunday, April 26

TimeEvent / Speaker
9:30 AM – 10:30 AM Tong Liu
On the reduction of crystalline representation via Kisin module.

Let K be a unramified p-adic field, G_K= Gal( Kbar/K) the absolute Galois group and T a Z_p-crystalline representation of G_K. I will explain the theorem of Bhatt-Gee-Kisin on the shape of Kisin modules for the reduction of T , and two approaches of this theorem: One by Bhatt-Gee-Kisin via prismatic F-gauge, and another approach by myself and Hui Gao via the classical theory of Kisin modules.
10:45 AM – 11:15 AM Zichuan WangTitle: Translation operations on trianguline (phi, gamma)-modules
11:30 AM – 12:30 PM Gleb Terentiuk
Fontaine-Laffaille modules and prismatic F-gauges

Drinfeld and Bhatt-Lurie developed a stacky approach to the prismatic (and syntomic) cohomology. In particular, for any p-adic formal scheme X, they attach a category of perfect complexes on the associated stack, called the category of F-gauges on X. This category has many interesting applications. For example, it is useful for understanding Galois representations arising from p-adic formal schemes. I will try to give an idea of what this category looks like in the case of the spectrum of Witt vectors of a perfect field of characteristic p. Namely, if one restricts to the Hodge-Tate weights [0, p-2], this category is equivalent to the derived category of Fontaine-Laffaille modules with the same restriction on Hodge-Tate weights. This is a joint work with Vologodsky and Xu.
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