The absolute Galois group of the rational number field is, of course, a central object in number theory.  However, it is known to be deficient in some respects.  In 1951, André Weil defined what came to be known as the Weil group.  This is a topological group refining the Galois group: it surjects onto the absolute Galois group with nontrivial connected kernel.  The Weil group provides an extension of the theory of Galois representations, allowing for a closer connection with automorphic forms.
In this course, I will explain that there remain further deficiencies of the Weil group, which must be corrected by a further refinement.  Our motivation comes from cohomological considerations, and the refinement we discuss is homotopy-theoretic in nature and goes in an orthogonal direction from the conjectural refinement proposed by Langlands (known as the Langlands group).  Yet, as we will explain, it does have relevance for the Langlands program.

The absolute Galois group of the rational number field is, of course, a central object in number theory.  However, it is known to be deficient in some respects.  In 1951, André Weil defined what came to be known as the Weil group.  This is a topological group refining the Galois group: it surjects onto the absolute Galois group with nontrivial connected kernel.  The Weil group provides an extension of the theory of Galois representations, allowing for a closer connection with automorphic forms.
In this course, I will explain that there remain further deficiencies of the Weil group, which must be corrected by a further refinement.  Our motivation comes from cohomological considerations, and the refinement we discuss is homotopy-theoretic in nature and goes in an orthogonal direction from the conjectural refinement proposed by Langlands (known as the Langlands group).  Yet, as we will explain, it does have relevance for the Langlands program.

The absolute Galois group of the rational number field is, of course, a central object in number theory.  However, it is known to be deficient in some respects.  In 1951, André Weil defined what came to be known as the Weil group.  This is a topological group refining the Galois group: it surjects onto the absolute Galois group with nontrivial connected kernel.  The Weil group provides an extension of the theory of Galois representations, allowing for a closer connection with automorphic forms.
In this course, I will explain that there remain further deficiencies of the Weil group, which must be corrected by a further refinement.  Our motivation comes from cohomological considerations, and the refinement we discuss is homotopy-theoretic in nature and goes in an orthogonal direction from the conjectural refinement proposed by Langlands (known as the Langlands group).  Yet, as we will explain, it does have relevance for the Langlands program.

Seed Seminar of Mathematics and Physics
Winter ’26: Flavors of Amplitudes 
The direct detection of gravitational waves has put the relativistic two-body problem in the spotlight and stimulated progress in perturbative approaches that provide analytic insight into its dynamics. Two strategies that have been witnessing interesting developments to this end are the ones based on scattering amplitudes, which apply to binary scatterings at large impact parameter, and on black-hole perturbation theory, which applies to extreme-mass-ratio binaries. In this talk, I will discuss how two very different kinds of differential equations have been playing a key role in such recent developments, in particular with the goal of characterizing the gravitational waves emitted and (re)absorbed by these systems.
Plus d’informations : https://seedseminar.apps.math.cnrs.fr/program/#february-18-2026
========
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.

Seed Seminar of Mathematics and Physics
Winter ’26: Flavors of Amplitudes 
To compute properties of phase transitions in condensed matter or the interactions of elementary particles, quantum field theory is typically solved perturbatively. This expansion produces divergent series, so the extraction of meaningful results (resummation) is not straightforward. In fact, very little is known about the actual asymptotic behaviour of these series. In this talk, I will introduce a new limit of quantum field theory (the „tropical“ limit), which is easily computable to very high orders in perturbation theory, yet at the same time captures the full complexity of subdivergences, renormalization, and scheme dependence. I will illustrate that the values of Feynman integrals and their tropical limit are highly correlated. Based on data up to 400 loops, we can precisely determine the asymptotic growth of the (tropical) beta function in different renormalization schemes. In particular, we find unexpectedly complicated instantons, and we confirm the absence of renormalons in the minimal subtraction scheme.
Plus d’informations : https://seedseminar.apps.math.cnrs.fr/program/#february-18-2026
========
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.

Seed Seminar of Mathematics and Physics
Winter ’26: Flavors of Amplitudes 
Perturbative calculations of string amplitudes are twofold: an expansion in the string coupling (the genus expansion of the worldsheet) and a low-energy expansion in the momenta. In this talk, I will focus on the low-energy expansion of closed string amplitudes at genus one, specifically for four- and five-point massless states of type IIB superstrings in flat spacetime. Evaluating these amplitudes involves integrating over the moduli space of punctured tori. I will demonstrate how the formalism of equivariant iterated Eisenstein integrals can be used to systematically calculate these integrals. Additionally, I will discuss the implications of these results for the S-duality of type IIB and conclude by exploring the underlying number-theoretic aspects of string amplitudes.
========
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
Winter ’26: Flavors of Amplitudes 
In this presentation, I will first review what purposes axiomatic quantum field theory serves and what the Wightman framework is and achieves. With that being done, I will address the question of the existence of the S-matrix in this framework, following a modern and dimension-independent approach to the Haag–Ruelle scattering; in doing so, I will put a special emphasis on the single-particle problem. With all this discussion having taken place in flat space, I will conclude by presenting some ongoing work on an AdS space version of these arguments.
 
========
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
Winter ’26: Flavors of Amplitudes 
I will talk about recent progress on the computation of gravitational waveforms directly from scattering amplitudes and field-theoretic techniques. I will present the general formalism and give an overview of new results. I will emphasise some technical aspects, such as the computation of the relevant integrals up to next-to-leading order in perturbation theory, and their structure in various limits.
========
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
Winter ’26: Flavors of Amplitudes 
Feynman integrals whose associated geometries extend beyond the Riemann sphere, such as elliptic and Calabi–Yau geometries, are becoming increasingly relevant in modern precision calculations. They arise not only in collider cross-section computations, but also in gravitational-waves scattering.                                                A powerful approach to compute such integrals is based on systems of differential equations, in particular when these can be brought into a canonical form, in which their singularity structure is manifest. In this talk, I will show that canonical Feynman integrals do enjoy similar properties, albeit different associated geometries, and I will illustrate how intersection theory can be used to further study and constrain the functions appearing in the amplitudes.
Plus d’informations : https://seedseminar.apps.math.cnrs.fr/program/#february-4-2026
========
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.

Organizing Committee: Daniel Baumann (Amsterdam and National Taiwan Univ.), Daniel Green (UC San Diego), Austin Joyce (Univ. of Chicago), Guilherme Pimentel (SNS Pisa).
Scientific Committee: Eiichiro Komatsu ((Max Planck Inst. for Astrophysics), Marilena LoVerde (Univ. of Washington), Eva Silverstein (Stanford Univ), Raman Sundrum (Univ. of Maryland).
The Summer School will be held at the Institut des Hautes Études Scientifiques (IHES) from July 6 to 17, 2026. IHES is located in Bures-sur-Yvette, south of Paris (40 minutes by train from Paris) – Access map
This school is open to everybody but intended primarily for young participants, including Ph.D. students and postdoctoral fellows. 
Deadline for applications: March 10, 2026

2026 IHES Summer School – Cosmological Correlators
The goal of this IHES school is to prepare students to make contributions to the study of cosmological correlations, both in the early and late universe. Theoretical cosmology as a discipline is increasingly crossing traditional subfield boundaries within high-energy physics. As a result, the full spectrum of topics and expertise students require cannot be simply contained in a single course.
This school aims to fill this gap by providing a holistic viewpoint on the diverse set of topics that students need to know, with an eye towards their applications in cosmology. There has been a remarkable amount of progress in the study of cosmological quantum field theory in the last few years, and a dedicated school focused on the diverse set of skills needed to contribute is much needed.
The school will have a set of courses given by world leaders in the subject, with the first week focused on EFT and bootstrap methods to compute cosmological correlators, and the second week devoted to more advanced topics and connections at the interface of particle theory and cosmology.
Speakers:

Dionysios Anninos (King’s College)
Scott Dodelson (Carnegie Mellon & Chicago Univ.)
Scott Melville (Queen Mary Univ. of London)
Enrico Pajer (DAMTP, Cambridge Univ.)
Claudia de Rham (Imperial College)
Marko Simonovic (Florence Univ.)
Charlotte Sleight (Univ. of Naples)
Massimo Taronna (Univ. of Naples)
Raffaele Tito D’Agnolo (IPhT CEA & ENS Paris)
Andrew Tolley (Imperial College)
Matias Zaldarriaga (IAS) 

 

 

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
I will begin this talk by reviewing asymptotic symmetries. I will then introduce a new symplectic structure and conservative boundary conditions at spatial infinity that accommodate regular logarithmic translations and log-supertranslations. The associated charges are finite and conserved, and I will show that the asymptotic symmetry algebra is an enhancement of the BMS algebra and that it acquires a central extension between supertranslations and log-supertranslations, which together form a Heisenberg algebra. I will conclude with some interesting avenues that this work opens.
 
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.

In this talk we will consider two families of representations from the fundamental group of a closed surface of genus at least 2 into the exceptional Lie group G2, and more precisely into its real split form G2′. Representations in these families correspond to Higgs bundles of a very special form introduced by Collier and Toulisse. They come with associated equivariant objects: they admit an alternating almost-complex map into the pseudosphere S2,4, which can be reinterpreted as a parallel distribution of planes along a minimal surface in the symmetric space.
From the Higgs bundle description of these families, however, it is far from clear whether these representations have good geometric properties. In joint work with Parker Evans, we use the equivariant objects to construct explicitly a geometric structure associated to some of these representations.
After an introduction to the geometry of G2′ and to these two families of representations, I will present our results explaining how to construct for every representation ρ in the first family a geometric structure modelled on a flag manifold of G2, the Einstein universe Ein2,3, whose holonomy is ρ. This is a structure on a fiber bundle over the considered surface with fiber diffeomorphic to Ein2,1.