In physics the spin of a particle determines its statistics. Furthermore, physical systems (in Euclidean signature) usually have a reflection structure, i.e. an identification of orientation reversal with complex conjugation. Neither of

L’étude des équations de la chaleur, des ondes, de Poisson entraîne l’émergence, dans la première moitié du 20ième siècle, des opérateurs à noyaux et des opérateurs différentiels. Ces équations sont usuellement de

Integrable differential-difference systems are endowed with biHamiltonian structures defined by difference operators, contrasting with the better known case of Hamiltonian PDEs. I will present a geometric framework for the investigation of such

The Hawking energy is one of the most famous local energies in general relativity, but it has the inconvenience that it is highly depedend on the surface taken.To remedy this Lamm, Metzger

In 2015, Chalykh and Silantyev observed that generalisations of the classical Calogero-Moser system with different types of spin variables can be constructed on quiver varieties associated with cyclic quivers. Building on their

A general procedure for non-abelinization of given integrablepolynomial differential equation is described. We are considering the NLStype equations as an example. We also find non-abelian Euler's top.Results related to non-abelian systems of

In this talk, we discuss a spectral perspective on the quantum diffusion conjecture for a quantum particle in a weakly random medium. We also draw the link to the study of Cherenkov

Dans cet exposé nous allons étudier deux analogues de la hiérarchie de Painlevé II : un intégro-différentielle et l'autre discret. Pour chacun de cas nous décrieront des solutions liées à une généralisation

It has been known for roughly 30 years that the Knizhnik--Zamolodchikov connection (KZ) can be obtained from the quantisation of the Schlesinger system: KZ controls correlation functions in conformal field theory, and

In mathematical physics, non self-adjoint operators and their associated evolution equations are used to model dissipative phenomena. In this talk, I will present some new results concerning the propagation of global analytic

We consider the focusing one-dimensional nonlinear Schrodinger equation (NLSE), which can be completely integrated using the Inverse Scattering Transform (IST) method. The IST allows decomposing of nonlinear wave fields into solitons and

Strongly-correlated systems are interesting yet hard to solve. However, even in the absence of the weak-coupling parameter, a theory might have a nice sector where it might become solvable. We found that

We present numerical and asymptotic results of our study of periodic blow-up solutions to the semilinear heat equation uₜ = uₓₓ + u² in the complex x-plane.  Time permitting, we'll also present

Dans cet exposé, j’expliquerai une application du formalisme des catégories de pré-Calabi-Yau à l’étude des espaces de lacets. On a développé ce formalisme avec Kontsevich et Vlassopoulos, comme un outil algébrique qui

https://indico.math.cnrs.fr/event/9726/

I introduce some basics of quantum information. The lecture covers the following topics: quantum circuits, Heisenberg picture in quantum computation, the stabilizer formalism, quantum error correction, and the Gottesman-Knill theorem. This series of

I introduce some basics of quantum information. The lecture covers the following topics: quantum circuits, Heisenberg picture in quantum computation, the stabilizer formalism, quantum error correction, and the Gottesman-Knill theorem. This series of

I introduce some basics of quantum information. The lecture covers the following topics: quantum circuits, Heisenberg picture in quantum computation, the stabilizer formalism, quantum error correction, and the Gottesman-Knill theorem. This series of

I will first outline the construction of an explicit algorithm transforming a post-Minkowskian (PM) metric in harmonic gauge to a metric in radiative gauges, such as Newman-Unti and Bondi gauges. Then, I

The UV/IR mixing problem makes renormalization difficult when considering quantum field theories on noncommutative spaces. To avoid the UV/IR mixing, Grosse and Steinacker adjusted the action of scalar Phi cubic theories on

After reviewing the elliptic quantum group $U_{q,p}(g)$ associated with the affine Lie algebra $g$, we introduce a new elliptic quantum toroidal algebra $U_{q,t,p}(gl_{1,tor})$. By using the vertex operators (the intertwining operators) of

The Bethe/Gauge correspondence of Nekrasov and Shatashvili describes the low energy dynamics of the vacua of certain supersymmetric gauge theories in terms of integrable spin chains. I will discuss an application of

I will report on recent advances in the definition of the solution theory to some singular stochastic PDEs, in connection with the construction of Euclidean QFTs. Hairer, in 2014, and Gubinelli-Imkeler-Perkowski, in 2015, have made

The semiclassical analysis of Bergman kernels is a multifaceted subject, with applications to physics, complex analysis, and geometry. Locally, the study of Bergman kernels can often be reduced to the analysis of

Local unitary invariant polynomials of tensor variables play an important role in the study of multipartite entanglement.  They also characterize tensor distributions that possess this invariance, and are in bijection with certain triangulations in dimension

In this talk, I will explain how to apply some standard integrability tools like Thermodynamic Bethe Ansatz (TBA) or Quantum Wronskian to realistic black holes models. In particular, the ringdown phase of

There are various ways to define braid groups $B_n$. One is to view it as the fundamental group of the configuration space of unordered $n$-points on the complex plane, and another is

An integrable system is often formulated as a flat connection, satisfying a Lax equation. It is given in terms of compatible systems having a common solution called the “wave function” $Psi$ living

Kekule structures are graphene-like lattices, with a modulation of the intersite coupling that preserves the hexagonal symmetry of the system. These structures possess very peculiar properties. In particular, they display topological phases

In this talk I will reconsider the no-hair theorems trying to understand two main aspects. First of all, no-hair theorems are always formulated in vacuum. However, it is legitimate to ask about the role that

We advocate for the existence of an alternative description of the scattering and gravitational radiation phenomena of black holes based on complex angular momentum techniques (analytic continuation of partial wave expansions, S-matrix

https://indico.math.cnrs.fr/event/10764/

In this talk I present an elementary derivation of the celebrated  Lee-Huang-Yang formula for Bose gases in the Gross-Pitaevskii Regime, which unifies various approaches that have been developed in recent years. We

Quasinormal modes are the gravitational wave analogue to the overtones heard after striking a bell. They dominate the signal observed during the ringdown phase after a dynamical event and are characterised by

We construct Hopf bimodules and Yetter-Drinfeld modules of Hopf algebroids as a generalization of the theory for Hopf algebras. More precisely, we show that the categories of Hopf bimodules and Yetter-Drinfeld modules

In this talk, I will present a construction of arbitrarily decaying initial data for the stability of Minkowski spacetime as solutions to the Einstein equations. Initial data on a spacelike hypersurface need

Les espaces de modules de connexions méromorphes sur les (fibrés principaux au-dessus des) surfaces de Riemann ont une structure géométrique très riche. Dans le cas logarithmique, ils coïncident avec les variétés de

A major modern problem in topological string theory is the studying of instanton moduli spaces, and their associated partition functions. We will try to explain the mathematical counterpart of this problem (Donaldson-Thomas

Reflection Equation Algebras (without parameters) are very remarkable objects. They admit introducing q-analogs of certain symmetric functions and quantum versions of some classical formulae of combinatorics:  Capelli, Frobenius and others. I plan

In this talk, I will present JT gravity and the Virasoro string, models of two-dimensional quantum gravity on constant negatively curved spacetimes and as two coupled CFTs, respectively, as models of random