Séminaire d’Analyse
A Jordan curve on the Riemann sphere can be encoded by its conformal welding homeomorphism, which is a circle homeomorphism. I will explain that this correspondence should be viewed as a canonical correspondence between a Jordan curve in the boundary of hyperbolic 3-space H3 and a positive curve on the boundary of AdS3 space.
The Loewner energy measures how far a Jordan curve is away from being a circle or, equivalently, how far its welding homeomorphism is away from being Möbius. It arises as the action of random curves SLE, Kähler potential of Weil-Petersson universal Teichmüller space, Fredholm determinant of Grunsky operator, free energy of Coulomb gas on a Jordan curve, and a renormalized volume of H3, etc. All these links refer to either the curve description or the welding description of the Loewner energy.
I will discuss two optimizing problems for the Loewner energy, one under the constraint for the curve to pass through n given points on the Riemann sphere and the other under the constraint for the welding curve to pass through n given points in the boundary of AdS3. These two problems exhibit many symmetries that are poorly understood, but do suggest that the Loewner energy sits right in the middle of two perspectives (curve/welding).
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

A framed polytope is the convex closure of a finite set of points in ℝⁿ together with an ordered linear basis. An n-category is a category that is enriched in the category of (n-1)-categories. Although these concepts may initially appear to be distant peaks in the mathematical landscape, there exists a trail connecting them, blazed in the 90’s by Kapranov and Voevodsky. We will traverse this path, widening and improving it as we address some of their conjectures along the way.
 
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

By commuting three vector fields on the line ℝ ∋ x with monomial coefficients 1, −2x, and −x2, we realise the Lie algebra sl(2) in its Chevalley basis; the bracket acts on the coefficients as the Wronskian determinant. Let us extend this model to a class of polynomial homotopy Lie algebras in which the N-ary brackets are given by the Wronskian determinants over multidimension; the generalised Vandermonde determinants then express the structure constants.
The alternated composition of N = 2p differential operators wj(x) ∂px of strict order p on the line ℝ ∋ x is again a differential operator of strict order p; its coefficient is the constant c(p) times the Wronskian determinant of the coefficients w1, …, wN. At p = 1, the sl(2) case fixes c(1) = 1; easy is c(2) = 2, then c(3) = 90. In a recent joint work with K. C. Shah, we reach the exact values c(p = 4) = 586 656, c(p = 5) ≈ 1.9 · 1012, and c(p = 6) ≈ 7.9 · 1021. The positive integer sequence c(p) seems to be new; to know c(p ⩾ 7) is an open problem.
Deform the binary Lie bracket to a formal sum of Wronskians with purely even (N = 2p) or arbitrary (N ∈ ℕ⩾2) arities, see arXiv:2510.02145 [math.RA]. Not only does the full bracket Δ satisfy the Jacobi identity Δ[Δ] = 0 for homotopy Lie algebra, but for every pair of arities ℓ, m ⩾ 2 the respective (ℓ, m)-term in the identity vanishes separately. Over base dimension d = 1, we spot an infinite sequence of finite-dimensional polynomial homotopy Lie algebras starting at sl(2) and with the Wronskians as the brackets; all the structure constants, unless zero due to repetitions, equal ±1 in a suitable basis.
Let the base dimension d ⩾ 1 be arbitrary: ℝd ∋ (x1,…,xd). We proved in arXiv:math.RA/04110185 that the complete generalised Wronskians – involving all the derivatives up to a given differential order k ⩾ 1 – still satisfy the table of Jacobi identities for strong homotopy Lie algebras. The arity N = (d+k  d) of such brackets grows with dimension d and order k but the steps, as k ↦ k + 1, grow as well: over d > 1 the gaps get larger and larger. In a recent work arXiv:2511.03848 [math.RA] we prove that by allowing the multivariate Wronskians be incomplete in their top differential order k > 1, we do preserve all the SH-Lie Jacobi identities.
For complete Wronskians of orders k ⩾ 1 over (multi)dimension d ⩾ 1 as the brackets, in a work in progress (joint with M. G. Ķēniņš) we exhaustively describe all the finite-dimensional polynomial N-ary SH-Lie algebra generalisations of sl(2); we express their structure constants in terms of the multivariate Vandermonde determinants. Relaxing the finite-dimensionality assumption and taking the (Laurent-)monomials in d variables for the generators, we obtain multivariate analogues of the Witt algebra from CFT.
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
The upcoming LISA mission will be sensitive to asymmetric binary black hole mergers. The self-force formalism generates waveform models by expanding in the small mass ratio, where accuracy requirements necessitate results up to second order. This problem is predominantly tackled with numerical methods, which are notoriously challenging. Complementing these methods with analytical approximations (e.g., around the Newtonian limit) can significantly reduce computational costs and yield independent benchmarks. Motivated by this, I will introduce analytical self-force theory and present the most recent advancements in second-order calculations. I will also present the latest version of the Teukolsky package within the Black Hole Perturbation Toolkit. This package has been greatly expanded to facilitate analytical calculations in self-force and black hole perturbation theory, and has recently found applications in scattering.
 
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

We show that two chain models of the gravity and the hypercommutative operads in genus zero are Koszul dual to each other. Precisely the model for the gravity operad is based on cacti without base points, and its bar construction arises from a cellular decomposition of the moduli space of stable curves. This is joint work with Tommaso Rossi.
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Radiation-reaction force encodes dissipative effects in a binary system emitting gravitational waves. Within the post-Newtonian framework, radiation-reaction terms enter the equations of motion starting at 2.5PN order and affect the system’s dynamics accordingly. These effects can be incorporated as corrections to the quasi-Keplerian orbital parameters in the center-of-mass frame. In this presentation, I will discuss the Lagrange method of variation of constants that we used to determine the radiation-reaction corrections for the quasi-hyperbolic orbit at 3.5PN order, and I will also report on our ongoing work at 4.5PN order.
 
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Séminaire d’Analyse
This is joint work with Baoxiang Wang (Jimei U.) and Zimeng Wang (Queen U.). We study the Cauchy problem of the Navier-Stokes equations in anisotropic spaces with critical or subcritical scaling. For the Lebesgue spaces, we obtain wellposedness for all exponents, while in the endpoint critical cases of the Sobolev or Besov space, we prove illposedness by norm inflation everywhere in the function space. Another endpoint of subcritical case is shown to be illposed by discontinuity everywhere of the solution map. Asymptotic profile of the inflation is given in terms of the linearized instability of the Kolmogorov flows for the Euler equation. We also give a full rigorous description of its spectra in two space dimensions.
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Seed Seminar of Mathematics and Physics
Spring ’26: TQFT and Knot Theory 
Graphical calculus provides a convenient way to represent objects and morphisms in a monoidal category using strands in the plane. This viewpoint extends naturally to more general surfaces and leads to constructions of TQFTs, such as the Turaev–Viro theories. In order to obtain oriented TQFTs, one usually uses a pivotal structure. In this talk, I will describe a more general approach based on a twisted pivotal structure, as predicted by the cobordism hypothesis. I will introduce a graphical calculus for these structures, which involves foliated surfaces and many drawings.
The zoom link is available by subscribing to the mailing list: sympa@listes.math.cnrs.fr
More information: https://seedseminar.apps.math.cnrs.fr/program/#april-29-2026
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

Séminaire d’Analyse
In this talk, we discuss some qualitative aspects of the dynamics of the Euler equation on a rotating sphere that are relevant or stratospheric flows. Zonal flow dominates the dynamics of the stratosphere and for most known planetary stratospheres the observed flow pattern is a small perturbation of an n-jet. Since the 1-jet and the 2-jet are stable, the main interest is the onset of instability for the 3-jet. We prove that the 3-jet is linearly unstable if and only if the rotation rate belongs to a critical interval. Turning to the nonlinear problem, we prove that linear instability implies nonlinear instability and that, as the rotation rate goes to infinity, nearby traveling waves change gradually from a cat’s eyes streamline pattern to a profile with no stagnation points. This talk is based on a joint work with Profs. Adrian Constantin, Pierre Germain and Zhiwu Lin.
========
Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe seminaire_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

The goal of this conference is to advance the dialogue and interactions between the LLM community and the larger world of mathematics in order to further the mathematical understanding of LLMs and contribute to solving some of the outstanding problems in the new field of LLMs.
 
In particular we intend to investigate mathematical structures that can be used to understand LLMs in terms of what they implicitly learn and how. 
 
At the same time, in the opposite direction the use of LLMs in order to do mathematics will be investigated.
 
Registration is free and open until May 20, 2026.
Invited speakers:Quentin Berthet (Google DeepMind)Edward Lockhart (Google DeepMind)Gabriel Peyré (CNRS, DMA, École Normale Supérieure)Yiannis Vlassopoulos (Athena Research Center & IHES)
Organizers: Michael Douglas (Harvard University & IHES), Amaury Hayat (CERMICS), Julio Parra-Martinez (IHES) and Yiannis Vlassopoulos (Athena Research Center & IHES)
The math and LLM day and the workshop on AI for the study of Amplitudes, are supported by the Google DeepMind AI for Math Initiative, and the IHES thanks Google DeepMind for their support.
 

Conjugacy classes in rank n affine Coxeter groups have a beautiful and simple geometric description in terms of their natural action on (n-1)-dimensional vector spaces. Moreover, one can locate the conjugating elements and centralizers in the vector space as well. These results allow to characterize the growth of the conjugator length function by geometric investigations.
 

Let S be a compact oriented surface with boundary, Γ its fundamental group, and G a simple algebraic group defined over Q such that the symmetric space associated to G(R) is Hermitian of tube type. Given a real closed field F and a canonical presentation of Γ, we define for a representation of Γ in G(F) an invariant taking values in an ordered abelian group A(F), called the refined Toledo invariant, as it generalizes the Toledo number in the case F = R. The group A(F) has a geometric interpretation as the group of signed areas for polygons in the Hilbert geometry associated to the upper half plane over F. The goal of the talk is to describe the construction of this invariant and to explain how it solves the problem of characterizing points in the real spectrum compactification of the space of maximal representations of Γ into G(R).