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
 
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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.
 
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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.
 

Gluing the opposite sides of a square gives a flat torus: a torus endowed with a flat metric induced by the Euclidean metric on the square. Similarly, one can produce higher genus surfaces by gluing parallel sides of several squares. These « square-tiled surfaces » inherit from the squares a flat metric with conical singularities. In this talk we will present several recent results and conjectures on the large genus asymptotics of these surfaces, and more generally of some families of flat surfaces (joint work with V. Delecroix, P. Zograf and A. Zorich). We will also see how these results can be interpreted in the language of closed curves on surfaces. We will finish with some recent results joint with E. Duryev and I. Yakovlev that should allow to generalize these results to a larger family of flat surfaces.
 

Séminaire de géométrie arithmétique
The mod-$p$ cohomology of equi-$p$-saturable pro-$p$ groups has been calculated by Lazard in the 1960s. Motivated by recent considerations in the mod-$p$ Langlands program, we consider the problem of extending his results to the case of compact $p$-adic Lie groups $G$ that are $p$-saturable but not necessarily equi-$p$-saturable: when $F$ is a finite extension of $mathbb{Q}_p$ and $p$ is sufficiently large, this class of groups includes the so-called pro-$p$ Iwahori subgroups of $SL_n(F)$. In general, using the work of Serre and Lazard one can write down a spectral sequence that relates the mod-$p$ cohomology of $G$ to the cohomology of its associated graded mod-$p$ Lie algebra $mathfrak{g}$. We will discuss certain sufficient conditions on $p$ and $G$ that ensure that this spectral sequence collapses. When these conditions hold, it follows that the mod-$p$ cohomology of $G$ is isomorphic to the cohomology of the Lie algebra $mathfrak{g}$.
 
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In this talk, I will show how to construct a holographic effective theory for the leading-twist multi-particle operators for $O(2)$ CFT in $d=3$ and $d=4-epsilon$. For $d=4-epsilon$ Wilson-Fisher fixed point. We obtain the Hamiltonian of the theory and show that it correctly reproduces all the dimensions at order ${mathcal O}(epsilon^2)$ of the leading twist operators for all values of the charge $Q$ and spin $J$. For $d=3$ strongly coupled $O(2)$ CFT, we find excellent agreement with $Q=3,4$ bootstrap data and inversion formula.
 
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Running Seminar
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
I will discuss the high-energy, small-angle limit of two-body classical gravitational scattering, focusing on the tower of multi-H diagrams that govern the leading logarithmic behavior. First, I will show that the recently developed SCET forward-scattering framework for gravity is fully equivalent to the multi-Regge expansion of the classical amplitude, reproducing exactly the s-channel multi-H diagrams. I will then compute the single-H diagram at two loops and the double-H diagrams at four loops, matching onto the classical eikonal phase in the ultrarelativistic limit. Finally, using dispersion relations, we establish a novel link between the high-energy logarithmic terms in the real and imaginary parts of the eikonal phase at 5PM order.
 
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Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Perturbative field theory calculations are essential for precision predictions in collider and gravitational-wave physics. One of the major bottlenecks in such calculations is integration-by-parts (IBP) reduction of the underlying Feynman integrals. In this talk, I will argue that IBP reduction can be simplified by exploiting the infrared singularity structure encoded in the Landau equations. More precisely, I will show that the IBP syzygy module decomposes as a sum over the Fitting ideals associated with the individual components of the Landau locus. This decomposition provides an efficient method for constructing syzygies and suggests universality of solutions among integral topologies sharing the same infrared structure.
 
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