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