Séminaire de géométrie arithmétique
The Cartier transform of Ogus and Vologodsky can be seen as a generalization of Cartier descent. It is an equivalence between modules with integrable connections on a smooth scheme over a perfect field of positive characteristic and Higgs modules on the Frobenius base change of this scheme. We discuss a generalization of this transform to log smooth schemes. More precisely, we discuss two generalizations of Shiho’s local version and Oyama’s crystalline-type version of this transform. For a log smooth scheme $X$ over a perfect field $k$ of positive characteristic, we obtain, under the assumption that the exact relative Frobenius lifts to the Witt vectors, a fully faithful functor from the category of quasi-coherent modules on the base change $X’=Xtimes_{k,F_k}k$ of $X$ equipped with a quasi-nilpotent Higgs field, to the category of quasi-coherent modules on $X$ equipped with a quasi-nilpotent integrable connection. In another direction and without any lifting assumptions, we construct a crystalline-type interpretation of this functor. To address the issue of essential surjectivity, we refine the topoi and crystals mentioned above by endowing them with an indexed structure, inspired by Lorenzon’s extension of Cartier descent to smooth logarithmic schemes.
 
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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
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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
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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.
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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.
 
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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.
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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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