We consider the model of an uncharged massive particle linearly coupled to a quantized radiation field, widely referred to as Nelson model. Despite having the character of a toy model from the

La journée d'équipe se tiendra en hybride: en salle rené Baire et sur TEAMS.Programme: 9h45-10h10 exposé de Nicolas Babinet 10h15-10h40 exposé de Eddy Brandon De León 10h45-11h Pause (café) 11h-11h25 exposé de

Semiclassical analysis can be employed to describe surface waves in an elastic half space which is quasi-stratified near its boundary. The propagation of such waves is governed by effective Hamiltonians on the

In this talk, it takes into account the KdV equation as an approximate model of long waves of small amplitude at the free surface with inviscid fluid. It is demonstrated that the

A quantum group is the mathematical structure responsible for the integrability of quantum systems, it has been formulated by Drinfeld and Jimbo in 1985. More recently, the refined notion of "shifted quantum

In their study of deformed W-algebras associated with complex simple Lie algebras, E. Frenkel-Reshetikhin (1998) introduced certain two parameter deformations of the Cartan matrices. They play an important role in the representation

I will present new results in the separation of variables (SoV) program for integrable models. The SoV methods are expected to be very powerful but until recently have been barely developed beyond

I will start with a brief review of large-N tensor models, and of some of their applications in theoretical physics. On the one hand, they provide a general platform to investigate random

I will briefly review the concept of magnetic quiver. It is a tool that allows the analysis of certain moduli spaces of physical theories. We will see how this can be used to attempt

Le resumé est disponible au format pdf en cliquant icihttps://indico.math.cnrs.fr/event/7153/

There is no notion of local gravitational energy density. Gravity manifests itself as curvature of spacetime, and its strength can be measured by using variations of the elementary geometric quantities (area, volume,

Statistical manifolds are family of density functions with respect to some measure endowed to geometric structures used to model information, their field of study belonging to Information Geometry, a relatively recent branch

Scattering theories are of great importance for many problems in General Relativity, and scattering in the interior of a black hole is particularly relevant in the context of the cosmic censorship conjecture

This talk concerns the (generalized) Soler model: a nonlinear (massive) Dirac equation with a nonlinearity taking the form of a space-dependent mass. The equation admits standing wave solutions and they are generally

Amplitudes predict the outcome of scattering experiments with particle colliders. Feynman's perturbative approach leads to considering a power series whose coefficients are computed by so-called Feynman integrals. The perturbative expansion of string

In this talk, I will explain how to compute both Hodge numbers for complete intersection Calabi-Yau (CICY) 3- and 4-folds using machine learning. I will first make a tour of various machine

Dans le domaine des équations aux dérivées partielles, les ondes solitaires sont des objets fondamentaux. Ces ondes aussi appelées solitons, qui gardent leur vitesse ainsi que leur forme au cours du temps,

A toute variété lorentzienne (M,g) est associée une structure « projective » induite par sa connexion de Levi-Civita. Dans certains cas, il est possible de réaliser M comme l’intérieur d’une variété à

Résumé : L'utilisation des algèbres de Leibniz à la place des algèbres de Lie en théorie de jauge est introduite de façon naturelle en supergravité. Les procédures de jaugeage dans ces théories

SO(3) transformations are key elements in physics, such as for controlled spin systems. In experiments we have to consider a large ensemble of such physical entities, which are not exactly identical :

I will discuss a recent result about the excitation spectrum of a dilute Bose gas. We start from the microscopic many-body Hamiltonian H_N of quantum mechanics and derive Bogoliubov’s prediction for the

We propose an adaptive inexact version of a class of semismooth Newton methods for variational inequalities.As a model problem, we study the system of variational inequalities describing the contact between two membranes.We

We consider 2d random ergodic Schrödinger operators with long range magnetic fields on domains with and without boundary. After a brief introduction to the bulk-edge correspondence in the quantum Hall effect, we

La cohomologie de Davydov-Yetter classifie les déformations infinitésimales des structures tensorielles (associateur d'une catégorie tensorielle ou d'un foncteur tensoriel). Après des rappels sur cette théorie cohomologique et quelques éléments d'algèbre homologique relative,

Résumé : In 1981, W.G. Unruh discovered a mathematical analogy between waves in condensed matter systems and massless scalar fields in a curved space-time. This discovery founded the field of analogue gravity

 La compréhension des constituants élémentaires de la matière avance grâce aux expériences où le résultat de collisions entre particules est comparé aux prédictions théoriques. Même si les diagrammes de Feynman permettent le

We consider the second best constant in the Hardy-Sobolev inequality on a Riemannian manifold. More precisely, we are interested with the existence of extremal functions for this inequality. This problem was tackled

Density functional theory (DFT) is one of the most used methods to model matter at microscopic scale in many-body quantum physics and chemistry. It can be expressed in terms of an inverse

Integrable nonabelian systems are equations of motion in which the field variables take values in a nonabelian algebra, as a matrix one. As their classical counterparts, we can describe their structure and

An important application of algebraic curves is in the context of integrable systems via multi-dimensional theta functions. They give rise for instance to solutions of  the Kadomtsev-Petviashvili hierarchy, a universal integrable system.This talk aims to make

In 1992, V. Turaev and O. Viro defined an invariant of smooth oriented closed 3-manifolds consisting of labelling the edges of a triangulation of the manifold with representations of 𝒰q(sl₂(ℂ)) (q being

In this talk, I am going to review some aspects of the current state of the art of Integrability in the AdS/CFT correspondence and beyond. I will first describe a general nonperturbative approach to

In this talk, we will study of the influence of the underlying space geometry on the asymptotic dynamics of the nonlinear Schrödinger (NLS) equation. We will consider the focusing NLS equation in

Abstract: Resonances are complex frequencies which describe the oscillation and damping of solutions to wave-type equations at large time scales.In black hole type spacetimes such as the De Sitter-Reissner-Nordström (DSRN) solution of

We describe a construction which to a surface and a Iwahori-Hecke algebra associates an invariant which is a Laurent polynomial. More generally, this construction works for surfaces with boundary and behaves well

I will show how to derive analytic gravitational waveforms associated to the coalescence of a “hairy” black hole binary in Einstein-scalar-Gauss-Bonnet gravity (ESGB). To this aim, I will first present the post-newtonian (PN) lagrangian

Many central problems in geometry, mathematical physics and biology reduce to questions regarding the behavior of solutions of nonlinear evolution equations. The global dynamical behavior of bounded solutions for large times is

One result of the fruitful interaction between Quantum Field Theory and Algebraic Geometry was the creation of Frobenius manifolds. Those objects lie at the heart of the mathematical vision of mirror symmetry

Un foncteur modulaire est un système cohérent de représentations des groupes de difféotopie des surfaces orientées. Le notion apparaît naturellement dans la théorie des représentations des groupes quantiques et dans la théorie

This talk will be dedicated to an averaging approximation (Rotating Wave Approximation) which allows to duplicate controls in the quantum setting by using quasi-resonant control fields. I will present some recent results