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.
 
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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.
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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.
 
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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.
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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
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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.
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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.
 

 
 

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. 
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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.
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