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).

Depending on nutrient availability, cells switch between two different modes: growth, which requires secretion, and conservation, which requires autophagy, a cellular recycling pathway. The mechanisms underlying the switch between these two modes are not clear. We propose that the evolutionary-conserved Ypt1/Rab1 GTPase, which is essential for the beginning of secretion and macro-autophagy pathways from yeast to human, coordinate this switch by functioning in two different “GTPase Modules” that include “pathway-specific” upstream activators and downstream effectors.     

Séminaire d’Analyse
We construct critical trajectories in kinetic geometry, i.e. curves in (t,x,v) that are tangential to the transport and v-gradient, connecting any two given points, respecting the underlying kinetic scaling, and matching scaling properties of the stochastic trajectories near the starting point. The construction is based on solving the laws of motions with a forcing made up of desynchronised logarithmic oscillations. These critical trajectories provide an  »almost exponential map » that allows to prove several functional analytic estimates. In particular they allow to extend to the kinetic setting the universal estimate for the logarithm of positive supersolutions by Moser 1971, and deduce optimal (weak) Harnack inequalities. This is a joint work with Helge Dietert, Lukas Niebel and Rico Zacher. 
========
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 will review the progress on the probabilistic theory of PDEs (random data, additive and multiplicative noise etc.) in recent years. Breakthrough has been made in the subcritical regime, first in parabolic settings, and then in dispersive settings, which also leads to better understanding of a number of important models. However, a number of challenges still exist. This talk is based on joint works with Bjoern Bringmann, Andrea Nahmod, and Haitian Yue.
========
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.

Let X be a regular, proper, flat and generically smooth scheme over the spectrum of a (strict) DVR S.
Bloch conjectured a formula which relates algebraic differential forms of X with the total dimension of the l-adic vanishing cohomology of X/S.
In this talk I’ll describe a proof of this formula using methods from non-commutative and derived algebraic geometry.
This is a joint work with Dario Beraldo.
 
========
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.

List of topics I want to present in a mathematically palatable language.
Life processes and information systems: from the cell to large language models (LLMs).Viruses: information storage, transmission, and evolution.Information warfare, organic poisons, infections, and immune systems.The central dogma (Crick): principal information flow in the cell; information reduction under protein folding.Metastability, catalysis, and signaling: signaling in cells, plants, animals, and humans.Information reduction and energy dissipation in epigenesis / development: the emergence of a chick from an egg.Information flows in animal nervous systems and the human brain: (broken) symmetries in olfaction, proprioception, somatosensation, vision, and audition.Modularity of circuitry in cells and in the brain.Poincaré–Sturtevant stochastic representations of geometry; object-dominated life-related (visual and non-visual) signals vs. stochastic continuity of abiotic signals.Stochastic generative combinatorics in languages.Information spaces and Kanerva’s sparse distributed memory (SDM) model.Artificial neural networks, information geometry, and orthogonal symmetries in LLMs.A mathematical perspective on learning, knowledge, and understanding.

List of topics I want to present in a mathematically palatable language.
Life processes and information systems: from the cell to large language models (LLMs).Viruses: information storage, transmission, and evolution.Information warfare, organic poisons, infections, and immune systems.The central dogma (Crick): principal information flow in the cell; information reduction under protein folding.Metastability, catalysis, and signaling: signaling in cells, plants, animals, and humans.Information reduction and energy dissipation in epigenesis / development: the emergence of a chick from an egg.Information flows in animal nervous systems and the human brain: (broken) symmetries in olfaction, proprioception, somatosensation, vision, and audition.Modularity of circuitry in cells and in the brain.Poincaré–Sturtevant stochastic representations of geometry; object-dominated life-related (visual and non-visual) signals vs. stochastic continuity of abiotic signals.Stochastic generative combinatorics in languages.Information spaces and Kanerva’s sparse distributed memory (SDM) model.Artificial neural networks, information geometry, and orthogonal symmetries in LLMs.A mathematical perspective on learning, knowledge, and understanding.