OpART workshop 2026 -- Saint-Dié-des-Vosges

Liste des Contributions

4. Power counting in noncommutative Quantum Field Theory

Eva-Maria Hekkelman (Max Planck Institute, Bonn)

26/05/2026 09:30

I consider Callias operators (that is, Dirac-Schrödinger operators perturbed by an operator-valued potential $A$) on odd, $d$-dimensional hyperbolic space. Without imposing uniform invertibility of the potential outside a compact region, the operators are no longer Fredholm, so that the Witten index, a type of regularized index defined via an iterated trace limit, becomes the natural...

1. Revisiting Singular Integrals: Applications to Subelliptic PDEs (Part I)

Brian Street (University of Wisconsin)

26/05/2026 11:00

Since work of Hilbert in 1908, singular integrals have played an important role in the study of PDEs. In the 1960s, Kohn and Nirenberg (building on work of Seeley, Unterberger, Bokobza) introduced pseudodifferential operators, which simplified many arguments that relied on singular integral operators. Since then, pseudodifferential operators have been used to great effect in the study of PDEs;...

5. The Satake groupoid for Riemannian symmetric spaces and beyond

Jacob Bradd (Université de Lorraine, Metz)

26/05/2026 15:00

With Nigel Higson and Robert Yuncken, we have constructed a groupoid for a Riemannian symmetric space, or $G/K$ where $G$ is a real reductive group with maximal compact subgroup $K$, based on a general construction due to Omar. Geometrically, it is formed as a smooth family of homogeneous spaces $G/H$, where $H$ ranges over all maximal compact subgroups (conjugates of $K$) and their "limit...

6. Seiberg-Witten equations on Hermitian symmetric spaces, part II

Rafailia Tsiavou (University of Thessaloniki)

26/05/2026 16:30

The Seiberg-Witten equations, originally formulated on a 4-dimensional manifold as the minima of a gauge-theoretic energy functional, have led to profound results regarding the differential structure of the manifold. In this second part, I will explain how representation theory can be used to formulate, generalise and solve these equations on Hermitian symmetric spaces and outline the idea...

7. On the algebraic Mackey deformation

Yvann Gaudillot-Estrada (Université de Lorraine, Metz)

26/05/2026 17:00

Let $G$ be a real reductive group with Lie algebra $\mathfrak{g}$ and let $K \subset G$ be a maximal compact subgroup.
The heart of the algebraic representation theory of $G$ consists in the study of $(\mathfrak{g},K)$-modules. The latter correspond to modules over a certain approximately unital ring $R$, known as the Hecke algebra of the pair $(\mathfrak{g},K)$. The contraction of $G$ onto...

2. Revisiting Singular Integrals: Applications to Subelliptic PDEs (Part II)

Brian Street (University of Wisconsin)

27/05/2026 09:30

Since work of Hilbert in 1908, singular integrals have played an important role in the study of PDEs. In the 1960s, Kohn and Nirenberg (building on work of Seeley, Unterberger, Bokobza) introduced pseudodifferential operators, which simplified many arguments that relied on singular integral operators. Since then, pseudodifferential operators have been used to great effect in the study of PDEs;...

8. High-frequency analysis of PDEs and pseudo differential calculus

Clotilde Fermanian (Université d'Angers)

27/05/2026 11:00

In this talk, we will discuss some traditional questions from PDEs on manifolds and explain the role of pseudo differential calculus in the manner they are solved. We will explain how to extend this approach on filtered manifolds and give example on contact manifolds and nilmanifolds.

9. Log-polyhomogeneous pseudodifferential operators on filtered manifolds and their spectral asymptotics

Edward McDonald (Universität Bonn / Université Paris Cité)

27/05/2026 15:00

A classical theorem of Euler is that a function $f$ on $\mathbb{R}^d$ is homogeneous of degree $m$ if and only if $Ef=mf,$ where $E$ is the Euler vector field. If we relax this to $Ef=mf+g,$ where $g$ is Schwartz-class, we say that $f$ is approximately homogeneous. Classical pseudodifferential operators have a symbol function $\sigma(x,\xi)$ which admits an asymptotic expansion into a series...

10. A regularity theorem for fully nonlinear maximally subelliptic PDEs

Gautam Neelakantan Memana (University of Wisconsin)

27/05/2026 16:30

Maximally subelliptic PDEs are a far-reaching generalization elliptic PDEs, and they enjoy many desirable properties analogous to elliptic PDEs. In this talk, we will discuss a sharp regularity theorem for a general fully nonlinear maximally subelliptic PDE in Sobolev spaces and recovering the regularity theorem for fully nonlinear elliptic PDEs as a special case.

11. Trace and Index of Callias Operators on Hyperbolic Space

Jilly Kevo (Universität Bonn)

27/05/2026 17:00

I consider Callias operators (that is, Dirac-Schrödinger operators perturbed by an operator-valued potential $A$) on odd, $d$-dimensional hyperbolic space. Without imposing uniform invertibility of the potential outside a compact region, the operators are no longer Fredholm, so that the Witten index, a type of regularized index defined via an iterated trace limit, becomes the natural...

3. Revisiting Singular Integrals: Applications to Subelliptic PDEs (Part III)

Brian Street (University of Wisconsin)

28/05/2026 09:30

Since work of Hilbert in 1908, singular integrals have played an important role in the study of PDEs. In the 1960s, Kohn and Nirenberg (building on work of Seeley, Unterberger, Bokobza) introduced pseudodifferential operators, which simplified many arguments that relied on singular integral operators. Since then, pseudodifferential operators have been used to great effect in the study of PDEs;...

12. Applications of operator algebras and operator theory to boundary value problems and layer potentials

Victor Nistor (Université de Lorraine, Metz)

28/05/2026 11:00

One of the main and oldest approaches to boundary value problems is through layer potentials. The study of layer potentials has lead, more than one hundred years ago, to the development of operator theory (including compact and Fredholm operators). The layer potential operators associated to a suitable boundary value problem on a smooth, bounded domain are pseudodifferential operators and, in...

13. Family index on contact fibrations and families of Toeplitz operators

Clément Cren (Universität Göttingen)

29/05/2026 09:30

At the end of the 80's, Boutet de Monvel gave an index formula for Toeplitz operators on certain complex domains. This formula was later re-interpreted by Epstein and Melrose using Heisenberg calculus on contact manifolds. In a joint work with Erfan Rezaei, we extend this formula to the case of families. More generally, we extend the index theorem of Baum and van Erp to families of contact...

14. Groupoid equivariant Roe algebras and coarse index map

Kai Mao (Université de Lorraine, Metz)

29/05/2026 11:00

In this talk we start with an introduction to Roe algebras and the coarse assembly map. Some difficulties appear when one is trying to define the groupoid equivariant analogue. We will share some techniques to formulate a framework to define groupoid equivariant Roe algebras and the coarse index map, and show that the coarse index map is compatible with the Baum-Connes assembly map for groupoids.

15. Localized equivariant index computations for manifold with boundary using groupoids

Mathis Alleysson (Université de Toulouse)

29/05/2026 11:30

In the second paper of the series "The Index of Elliptic Operators", M. Atiyah and G. Segal study the G-equivariant topological index associated with the action of a compact Lie group G on a manifold. After localization at a conjugacy class, this index can be expressed in terms of fixed-point data, leading to Lefschetz-type fixed point formulas. In this talk, we study this localized...