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

We construct a cubic cut-and-join operator description for the partition functions of all semi-simple cohomological field theories, and, more generally, for the partition functions of the Chekhov-Eynard-Orantin topological recursion on a possibly

Abstract:The spectral theory of non-selfadjoint operators is an old and highly developed subject. Yet it still poses many new challenges crucial for the understanding of modern problems such as scattering systems, open

Through the Reshetikhin-Turaev construction, a three-dimensional topological field theory can be built from a semisimple modular category. Thanks to a result of Bartlett, Douglas, Schommer-Pries and Vicary, a semisimple modular category is

In a recent article, Betea, Bouttier and Walsh presented a relation between higher order analogue of Tracy-Widom distribution and certain Toeplitz determinants describing the discrete gap probabilities in a multicritical random partitions

We discuss the 5d AGT correspondence of supergroup gauge theories with A-type supergroups. We introduce two intertwiners called positive and negative intertwiners to compute the instanton partition function. The positive intertwiner is

https://indico.math.cnrs.fr/event/8776/

String field theory is a second-quantized formulation of string theory. While its general properties are well understood, its action is non-polynomial and requires the determination of complicated subspaces of the moduli spaces

The Fröhlich polaron describes the slow movement of an electron in a polar crystal. A long open problem is the asymptotics of the effective mass of the polaron in the strong coupling

Noncommutative associative star-products are deformations of the usual product of functions on smooth manifolds; in every star-product, its leading deformation term is a Poisson bracket. Kontsevich's star-products on finite-dimensional affine Poisson manifolds

https://indico.math.cnrs.fr/event/8660/

The bismash product $H_n = mathbb C^{C_n}#mathbb CS_{n−1}$ and its dual $J_n = mathbb C^{S_{n−1}}#mathbb CC_n$ are semisimple Hopf algebras whose structure is induced from a factorization of the symmetric group $S_n

https://indico.math.cnrs.fr/event/8661/

I will review some recent developments in the investigation of the asymptotic structure of general relativity, and in particular the various extensions of the asymptotic symmetry group which have been proposed in

Marc Geiller (ENS Lyon), who will be our speaker for the mathematical physics seminar of Dec 7, has agreed to give an additional informal talk on Friday Dec 9, at 10am in

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/