Workshop 2025 ANR OpArt

15 déc. 2025, 08:00 → 17 déc. 2025, 18:05 Europe/Paris

Albi, Institut national universitaire Jean-François-Champollion

Ce atelier de travail de l'ANR OpArt se tiendra du Lundi 15 décembre 9h au mercredi 17 décembre à l'Institut National universitaire Jean-François Champollion d'Albi.

La rencontre est l'occasion pour les membres du projet ANR et les jeunes chercheurs en lien avec le projet de présenter leurs travaux, tout en ménageant du temps pour favoriser les intéractions. 

Soutiens financiers :

• Projet ANR OpArt (ANR-23-CE40-0016)
• L'Université Paris Est Créteil
• Le réseau thématique du CNRS Trétraèdre 
• L'Institut de Mathématiques de Toulouse
• L'Institut National Universitaire Jean-François Champollion

 

Organisateurs :

• Alain Berthomieu (INJC/IMT Albi)
• Paulo Carrillo Rouse (IMT)
• Jean-Marie Lescure (UPEC)

 

lun. 15 décembre

09:00 Accueil, Café, Thé et viennoiseries -- Welcome, Coffee, Tea and pastries

1 Calcul de traces de projecteurs dans des C*-algèbres de groupoïdes

Je présenterai une construction géométrique du projecteur de Rieffel de
la C*-algèbre de la rotation irrationnelle et le calcul de sa trace.

Orateur: Jean Renault

2 Harish-Chandra’s philosophy of cusp forms via Lie groupoids

Harish-Chandra spent his career understanding the unitary representations of real reductive Lie groups like SL(n,R). One of the crucial points in this theory is his "philosophy of cusp forms", which says that any tempered unitary representation of a real reductive group (with compact centre) is either discrete series, meaning it is a subrepresentation of the regular representation, or it is induced from a parabolic subgroup, such as the block upper-triangular subgroup in SL(n,R). This sets up an inductive argument over ever smaller subgroups. I will describe how Harish-Chandra’s principal follows from a Lie groupoid construction due to Omar Mohsen plus some C*-algebra theory.
(Joint work with Jacob Bradd and Nigel Higson)

Orateur: Robert Yuncken

3 Generalised Kontsevich-Vishik trace associated with a graph

I shall report on ongoing work with S. Scott and B. Zhang by which we
generalise regularised spectral zeta functions to a generalised
Kontsevich-Vishik trace associated with a Feynman graph. These in turn
generalise Feynman amplitudes on a Riemannian manifold studied by
Dang and Zhang [JEMS 2021] in two ways. Whereas they consider graphs
decorated by a single Riemannian Laplacian on a Riemannian manifold, we
consider a general closed manifold and decorate the edges of the graph
with arbitrary classical pseudo-differential operators. Whereas Dang
and Zhang use complex powers of the Laplacian to regularise, we
consider general holomorphic perturbations of the operators decorating
the edges. Similarly to their approach, our method involves several
complex parameters in the spirit of analytic renormalisation by Speer.
We claim that the resulting regularised Feynman amplitudes admit
analytic continuation as meromorphic germs with linear poles in the
sense of the works of Guo, Paycha and Zhang. We give an explicit
determination of the affine hyperplanes supporting the poles, which only
depends on the Betti number of the graph and the orders of the
operators. Neither the poles nor the method by which we determine them
make use of the underlying geometry of the manifold.

Orateur: Sylvie Paycha

12:45 Déjeuner -- Lunch

4 Sessions de travail -- Working sessions

16:00 Goûter -- Coffee Break

5 The Mackey analogy as a stratified equivalence

The Mackey analogy refers to a correspondence between the tempered representation theory of a real reductive group $G$ and that, much simpler, of its associated Cartan motion group $G_0$. It takes the form of a bijection, due to Higson in the complex case and Afgoustidis in the general case, between the tempered duals of these groups, which preserves certain invariants. With Nigel Higson and Angel Román, we constructed an embedding of C-algebras $C^\ast(G_0)\longrightarrow C^\ast_r(G)$, which characterizes the bijection and induces the Connes-Kasparov isomorphism. After briefly reviewing the correspondence and its C-algebraic aspects, I will report on joint work with Afgoustidis on the properties of the embedding. We will see that it preserves certain natural stratifications on the tempered duals of $G$ and $G_0$ respectively, shedding a new light on the topological properties of the Mackey bijection.

Orateur: Pierre Clare

6 Exposé -- Talk

Orateur: Edward McDonald

mar. 16 décembre

7 Exposé -- Talk

Orateur: Clément Cren

8 Exposé -- Talk

Orateur: Paul Le Breton

10:45 Pause Café -- Coffee Break

9 Exposé -- Talk

Orateur: Lucas Lemoine

10 Exposé -- Talk

Orateur: Florian Thiry

12:45 Déjeuner -- Lunch

11 Sessions de travail -- Working sessions

16:00 Pause Café -- Coffee Break

12 Stability by functional calculus of the algebra of smooth functions with compact support

For which Lie groupoid $G$ is the convolution algebra $C_c^\infty (G)$ stable by holomorphic functional calculus in $C^*(G)$? We will answer this question completely. In particular, we will show that this is the case if the groupoid $G$ is proper.
Joint work with Claire Debord and Kévin Massard

Orateur: Georges Skandalis

13 Exposé -- Talk

Orateur: Omar Mohsen

mer. 17 décembre

14 Exposé -- Talk

Orateur: Jacob Bradd

15 Exposé -- Talk

Orateur: Alessandro Contini

10:45 Pause Café -- Coffee Break

16 Exposé -- Talk

Orateur: Iakovos Androulidakis

12:15 Déjeuner -- Lunch