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

(The talk will be given in English in case non-French speakers are attending)Les effets de rotation et de stratification en densité (e.g. quand un fluide léger se trouve au dessus d'un fluide

Les cartes bicolorées peuvent être comprises comme un cas particulier du modèle d'Ising sur les cartes. Elles contiennent une complexité combinatoire qui n'est pas présente dans les cartes quelconques, et qui se

Recently, I introduced a non-perturbative quantization of impulsive gravitational null initial data. In this talk, I present the key results established thus far. The starting point is the characteristic null initial problem for tetradic gravity

In the middle of 1980's, motivated by study of singularity theories, K. Saito introduced the notion of "elliptic root systems". Roughly speaking, they are root systems with two null directions. Furthermore, he

The polaron describes a charged particle moving in a polarizable medium. Due to the interaction with the medium, the particle appears to be heavier that it would be outside the medium. This

La résolution des EDO avec des singularités irrégulières en domaine complexe peut être faite soit formellement, soit analytiquement. Au niveau formel, une méthode de Poincaré permet de construire un frame de solutions

The coalgebra symmetry method, developed by is one of the most fruitful techniques to produce systematically an N-dimensional Hamiltonian integrable system from a 1-dimensional system. This method has been recently adapted for

How are bulk strings related to boundary Feynman diagrams? I will give an overview of my work with Rajesh Gopakumar on deriving the closed string dual to the simplest possible gauge theory,

I will talk about models of two dimensional random growth (namely, polynuclear growth) which can be translated into probability laws on integer partitions by way of the RSK algorithm. As a consequence,

The local information of a 2d rational conformal field theory (RCFT) is encoded in a vertex operator algebra, whose modules constitute a modular fusion category C. The collection of global observables of

Recently, the study of higher categories of topological defects in quantum field theory has gained significant attention due to their connection to categorical symmetries. These higher categories exhibit noteworthy additional structures, depending

Cosmic strings (or vortex strings) are topological defects arising when U(1) symmetry is spontaneously broken in quantum field theories. In three-dimensional relativistic systems, loops of cosmic strings are known to be unstable

Four-dimensional Wess-Zumino-Witten (4dWZW) models are analogous to the two dimensional WZW models and possesses aspects of conformal field theory and twistor theory .  Equation of motion of the 4dWZW model is the

A fundamental prediction of quantum physics is the existence of random fluctuations everywhere in vacuum. This is one of the most remarkable and central ideas in quantum field theory which manifests itself

The prominent role of matrix models in physics and mathematics is well known. It is especially interesting that some of those models are exactly solvable, meaning the one can find explicit formulas

Spin chain are quantum-mechanical models for magnetic materials. Special examples are (quantum) integrable: they have many conserved charges whose spectrum can be determined exactly thanks to a rich underlying algebraic structure. While

Conformal field theory (CFT) plays a crucial role in understanding phase transitions, whether quantum or statistical. Typically, CFTs are studied using perturbative methods, such as the 4-epsilon expansion and the large N

In this presentation, we explore the local exact controllability to a constant trajectory for the compressible Navier-Stokes-Korteweg system on the torus in dimensions $din{1,2,3}$, where the control acts on an open subset.

This is the third edition of the research network workshop of Dijon-Lyon-Metz on mathematical physics. Topics of the workshop include (but are not restricted to):Classical and Quantum Field Theory (multisymplectic geometry, Higher

We study an inverse resonance problem on a radially and compactly perturbed infinite hyperbolic cylinder. Using the symmetries of this kind of geometry, we are led to study a stationary Schrödinger equation

https://indico.math.cnrs.fr/event/12325/

Invited speakersKen Shiozaki (Kyoto University)Atsushi Ueda (Ghent University)Hidir-Deniz Yeral (Université de Bourgogne)https://indico.math.cnrs.fr/event/12725/

Conformal geometry tools allow us to study global geometric aspects of a spacetime using local differential geometry. In this talk, I will focus on a particular conformal representation of Minkowski spacetime which

La dualité $x$-$y$, depuis sa découverte comme une symétrie de la récurrence topologique de Eynard-Orantin, a été l'objet principal d'investigations dans des domaines divers (systèmes intégrables, théorie des cordes, géométrie algébrique et

V. Drinfeld defined the KZ associator by considering the regularized holonomy of KZ equation along the real interval from 0 to 1 and proved that it satisfies the pentagon equation.  We consider

We elucidate the relationship between 2d integrable field theories and 2d integrable lattice models, in the framework of the 4d Chern-Simons theory. The 2d integrable field theory is realized by coupling the