CATS 8 - A conference in honour of Gabriele Vezzosi's 60th birthday

Titles and abstracts

10. Relative Brauer groups of finitely generated extensions: a geometric approach

Vistoli

28/09/2026 09:30

I am going to report on joint work in progress with Giulio Bresciani, Zinovy Reichstein and ChatGPT.
If L/K is a field extension, the relative Brauer group Br(L/K) is the group of classes in the Brauer Br(K) that vanish in Br(L). If L is finitely generated over K, we can think of L as the field of rational functions on an algebraic variety M over K.
In the first part of my talk I will...

11. Synthetic Betti realization

Haine

28/09/2026 11:00

Let X be a complex variety. In Deligne’s work on Hodge theory, he explained how to use the algebraic structure of X to endow the rational Betti cohomology H∗(X(C); Q) with a functorial increasing weight filtration. Deligne’s construction of the weight filtration is quite ingenious, and it isn’t a priori clear if the weight filtration can be refined to a filtration on the integral Betti...

12. Arcs with values in the projective line

Maffei

28/09/2026 16:50

Motivated by a construction of a work of Melani, Nocera and Vezzosi on G torsors on surfaces we study the space of arcs with values in the projective line.

13. On the Bloch conductor formula

Beraldo

28/09/2026 18:20

I will discuss a proof of a generalization of the Bloch conductor conjecture, obtained in joint works with Massimo Pippi. The proof exploits several innovative ideas of Bertrand Toen and Gabriele Vezzosi.

14. On Quillen’s finiteness conjecture for the cotangent complex in characteristic two

Schürg

29/09/2026 09:30

Quillen made two finiteness conjectures on the cotangent complex. The first is now known as Avramov’s theorem, the second is still open in general. In characteristic two, Turner proved Quillen’s second conjecture over a Cohen-Macaulay base. In the talk, I’ll outline a strategy to improve Turner’s approach to an arbitrary base using tools from derived algebraic geometry. This is work in progress.

15. The Darboux stack of a (-1) symplectic Artin stack

Robalo

29/09/2026 11:00

In this talk I will report on joint work with Hennion extending the contractibility of the stack parametrizing local Darboux models for (-1) symplectic derived Artin stacks, extending previous results with Hennion and Holstein for schemes and DM stacks.
Applications will be discussed.

16. Integral structures on Hodge atoms

Pantev

29/09/2026 16:50

I will describe a novel formalism for defining and
specifying integral structures on the tt^*-geometries that
parametrize massive vacua in N=2 QFTs. I will focus on non-archimedean
variants of these structures which arise naturally in complex
geometry and mirror symmetry and are known as F-bundles, and on their
basic pieces known as Hodge atoms. I will explain a construction of
the...

22. Deformation of algebraic cycles and the motive of the affine line

Elmanto

29/09/2026 18:20

Bertrand and Gabriele introduced to the world a derived algebraic geometry way of thinking about coefficients for cohomology theories, starting with their treatment of chern characters, mixed graded complexes and sheaves on the loop space. Taking inspiration from this story, I want to present a way to describe the deformation theory of motivic cohomology and algebraic cycles using a...

20. Poster Session

29/09/2026 20:50

18. Categorical topological algebra: Tate vs solid

Pourcelot

30/09/2026 09:30

In formal geometry, one naturally encounters complete algebras of
various kinds. This raises the question of how to deal with these
topological objects, at the derived level.
I will review two categorical frameworks which answer this question:
- the first one is that of Tate modules (introduced by Drinfeld
following Beilinson, and Hennion at the derived level);
- the second is the theory...

21. Ext algebras of subvarieties, formal geometry, and formality theorems

Calaque

30/09/2026 11:00

In this talk, I will present ongoing work with Alex Vitanov aimed at describing the Ext algebra of the sheaf associated with a closed embedding of smooth algebraic varieties.
I will first recall the case of the diagonal embedding, and then explain the two main tools we use:
- methods from formal geometry in a relative setting;
- a formality theorem in the presence of branes.
If time...

17. The Hochschild--Konstant--Rosenberg theorem for DM stacks

Scherotzke

01/10/2026 09:30

We prove a Hochschild--Konstant--Rosenberg (HKR) theorem for arbitrary derived Deligne--Mumford (DM) stacks. To this aim, we introduce the notion of orbifold inertia stack of a derived DM stack; this supplies a derived enhancement of the classical inertia stack, which does not always coincide with the classical truncation of the free loop space. We show that, in characteristic $0$, given a...

23. Height one phenomena in p-adic Hodge theory

Moulinos

01/10/2026 11:00

The syntomification of the integers (Z_p^syn) acts as a parameter space for p-adic cohomology theories. By the work of Drinfeld and others, it is known to carry a canonical formal group, and hence a map to the moduli stack of formal groups. Pulling back along this map gives rise to a certain line bundle equipped with a distinguished section "v_1". On the p-completed moduli stack of formal...

25. Algebraic infty-categories, Theta-structures and tannakian duality

Toen

01/10/2026 16:50

(Joint with Nuiten and Vezzosi) I'll explain the words in the title and state a general tannakian duality relating certain infty-stacks ("tannakian gerbes") with certain algebraic symmetric monoidal infty-categories with Theta-structures ("tannakian Theta-categories"). Possible applications to motives and to the "exponential homotopy theory".

24. Categorification of the assembly maps

Nocera

01/10/2026 18:20

Let G be a finitely presented torsionfree group and R a regular ring. The K-theoretic assembly map is a morphism of spectra between the homology of BG with coefficients in the nonconnective algebraic K-theory spectrum of R to nonconnective algebraic K-theory of the group ring RG. The L-theoretic assembly map plays a similar role for quadratic L-theory. The Farrell--Jones Conjecture says that...

19. Special Talk

01/10/2026 20:50

26. Deformation theory of the moduli superstack of stable maps

Pavia

02/10/2026 08:45

Supergeometry is the natural mathematical framework that accommodates the notion of supersymmetry in theoretical physics and string theory. In the last dozen years, this field of research has found a renewed popularity after the foundational work of Donagi and Witten, who proved that super moduli spaces of super Riemann surfaces cannot be straightforwardly recovered and studied starting from...

27. Degenerations in nonabelian Hodge theory

Simpson

02/10/2026 09:45

Given a family X/S we can form various kinds of nonabelian cohomology spaces relative to the base. When there are singularities, these undergo some kind of degenerations. We will look at some aspects of this question including higher or secondary monodromy, weight filtrations and Hodge or twistor structures, and the difficulties involved in some parts of the desired constructions.