Workshop 2025 ANR OpArt

Liste des Contributions

9. Calcul de traces de projecteurs dans des C*-algèbres de groupoïdes

Jean Renault

15/12/2025 09:45

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

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

Robert Yuncken

15/12/2025 10:45

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...

5. Generalised Kontsevich-Vishik trace associated with a graph

Sylvie Paycha

15/12/2025 11:45

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...

16. The Mackey analogy as a stratified equivalence

Pierre Clare

15/12/2025 16:30

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...

7. The trace theorem on Carnot manifolds

Edward McDonald

15/12/2025 17:30

The algebra of pseudodifferential operators affiliated to a Carnot manifold has a natural trace which is a generalisation of the Guillemin-Wodzicki residue constructed by Dave-Haller and Couchet-Yuncken. I will explain why this residue coincides with the Dixmier trace.

17. Factorization of the Dirac Operator on Foliations

Lucas Lemoine

16/12/2025 09:00

On a foliation induced by a Riemannian submersion, J. Kaad and W. D. van Suijlekom constructed two natural operators whose product is the Dirac operator, up to a bounded curvature term. This result gives a geometric outlook on the work of A. Connes, M. Hilsum, and G. Skandalis about wrong-way functoriality in bounded KK-theory, where this curvature term remained implicit.
In this talk, using...

23. Sub riemannian tangent spaces and groupoids

Paul Le Breton

16/12/2025 09:45

A sub-riemannian structure on a manifold $M$ naturally produces a distance $d_{CC}$. The study of the metric space $(M,d_{CC})$ raises 2 natural questions:
- For $x \in M$ is there a metric space that encodes the infinitesimal properties of the structure at $x$ as does the tangent space $(T_xM, g_x)$ in riemannian geometry ?
- If such a space exists what kind of algebraic structure can it be...

21. Geometric obstructions to fully ellipticity for families with embedded corners

Florian Thiry

16/12/2025 11:00

First we present how K-theory can be used to express obstruction to fully ellipticity from ellipticity. Then we set a geometrical context, namely families of manifold with embedded corners and we introduce some tools related to it (as cononormal homology, Monthubert groupoid for families, ...). Finally we compute the fully ellipticity obstruction in this context in terms of smaller indices and...

11. Stratification of the Helffer-Nourrigat Cone

Clément Cren

16/12/2025 11:45

Given a sub-riemannian manifold (or singular filtrations of the tangent bundle), Androulidakis, Mohsen and Yuncken constructed a calculus adapted to the corresponding hypoelliptic problems arising from the filtration. The principal symbol of an operator then becomes a family of operators in representations of nilpotent groups, the osculating groups (there is one attached to each point of the...

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

Georges Skandalis

16/12/2025 16:30

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

14. Functional calculus

Omar Mohsen

16/12/2025 17:30

3. Tempiric representations and the Connes-Kasparov isomorphism

Jacob Bradd

17/12/2025 09:00

(With Nigel Higson and Robert Yuncken.) An important result of Vogan in representation theory for real reductive groups states that if $K$ is a maximal compact subgroup of a real reductive group $G$, then the tempered irreducible representations of $G$ with real infinitesimal character (the "tempiric" representations, as coined by Afgoustidis), up to equivalence, are in bijection with...

19. Algebras and states in QFTs with timelike boundaries

Alessandro Contini

17/12/2025 10:00

Based on ongoing work with Alexander Strohmaier, we review the algebraic approach to quantum field theory on curved spacetimes in the presence of a timelike boundary. In particular, we look at quasi-free states which are determined by their action on pairs of observables, and introduce a notion of Hadamard states in this context: they are bisolutions to the mixed Dirichlet-Cauchy problem for a...

24. Towards a comparison of Geometric Quantization with Deformation Quantization

Iakovos Androulidakis

17/12/2025 11:15

E. Hawkins proposed a scheme for geometric quantization of a Poisson
manifold by means of deformation to normal cone of a symplectic groupoid,
where the C*-algebra involved is twisted by polarization. We report on
work in progress with P. Antonini, F. Bonechi, N. Ciccoli and V. Zenobi,
where we review these ideas using a natural filtration. We redefine the
notion of polarization allowing...

22. Accueil -- Welcome

1. Accueil, Café, Thé et viennoiseries -- Welcome, Coffee, Tea and pastries

Accueil des participants, café, thé et viennoiseries

Welcome for participants, coffee, tea and pastries

4. Déjeuner -- Lunch

12. Déjeuner -- Lunch

20. Déjeuner -- Lunch

2. Exposé -- Talk

6. Goûter -- Coffee Break

10. Pause Café -- Coffee Break

15. Pause Café -- Coffee Break

18. Pause Café -- Coffee Break

25. Sessions de travail -- Working sessions

26. Sessions de travail -- Working sessions