Running Seminar
The argument–shift method constructs maximal Poisson-commutative subalgebras of the symmetric algebra $S(mathfrak g)$ of a Lie algebra $mathfrak g$ with respect to the Lie–Poisson bracket. Their quantizations—known as quantum argument–shift subalgebras—form maximal commutative subalgebras of the universal enveloping algebra $U(mathfrak g)$ and play a fundamental role in quantum integrable systems. Although existence and uniqueness of these quantizations have been established in many cases, the underlying argument–shift procedures, realized as derivations of $S(mathfrak g)$, had not previously been quantized. Recently, Yasushi Ikeda and I defined quantized argument–shift procedures for $mathfrak{gl}_n$ and proved that they generate the associated quantum argument–shift subalgebras.
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Symmetry and Topology in Particle Physics    March 9-12, 2026    at IHES – Marilyn and James Simons Conference Center    How to get to IHES

 
In the past decade, sweeping progress in our understanding of quantum field theory (QFT) has revealed new organizing principles whose impact is already being felt across high energy, condensed matter, and mathematical physics. These include the generalization of the conventional principle of symmetries to include those that act on extended objects and/or do not come with an inverse. The goal of this workshop is to bring these new theoretical developments to bear on the problems of particle physics. The workshop aims to establish a new bridge between the formal and phenomenological high-energy physics communities, which will drive progress in both directions. 
 

 
Organizers:
Lea Bottini (IHES), Julio Parra Martinez (IHES), Alessandro Podo (IHES), Giovanni Rizi (IHES)
Scientific Committee:
Nathaniel Craig (UCSB), Clement Delcamp (IHES), Henriette Elvang (Michigan), LianTao Wang (Chicago)
Invited speakers:

Daniel Brennan (University of Birmingham)

Yichul Choi (Institute for Advanced Study)

Clay Cordova (University of Chicago)

Lucia Cordova (CERN)

Nathaniel Craig (UC Santa Barbara)

Raffaele Tito D’Agnolo (IPhT, CEA Saclay/ENS)

Isabel Garcia Garcia (University of Washington)

Diego Garcia-Sepulveda (Harvard University)

Sungwoo Hong (KAIST)

Po-Shen Hsin (King’s College London)

Seth Koren (University of Notre Dame)

Ho-Tat Lam (Stanford University) REMOTE TALK
Vazha Loladze (Oxford University)

Riccardo Rattazzi (EPFL)

Mario Reig (CERN)

Ling-Xiao Xu (ICTP)

 

Japanese-French Conference on Arithmetic Geometry in Honor of Takeshi Saito and Takeshi Tsuji        May 31 – June 4, 2027 at IHES – Marilyn and James Simons Conference Center    How to get to IHES

This conference, which is part of a long-standing tradition of French-Japanese collaboration in arithmetic geometry, will honor two leading figures of this partnership: Professor Takeshi Saito, on the occasion of his retirement, and Professor Takeshi Tsuji, on the occasion of his 60th birthday.
The main topics of the conference will include:

p-adic Hodge theory, including the p-adic Simpson correspondence, geometric Sen theory, p-adic Galois representations and (φ,Γ)-modules, prismatic cohomology, and their applications;

Ramification theory, including singular support and characteristic cycles of l-adic étale sheaves (in equal and mixed characteristic), compatibility with proper higher direct images, Swan conductors, and epsilon-factors;

Geometric Langlands theory, l-adic, p-adic, and for modules with integrable connections, in characteristic p and in characteristic 0.

 
Invited speakers:
Organizers: 

Ahmed Abbes (CNRS, IHES)
Laurent Berger (ENS de Lyon)
Takashi Hara (Tsuda University)
Atsushi Shiho (University of Tokyo)
Yuri Yatagawa (Institute of Science Tokyo)

Running Seminar
In my talk, I will introduce several sets of central elements in the universal enveloping algebra U(glN) and explain the relationships between them using average value of the gl-weight system as an example. As a consequence, we obtain a proof of the M. Kazarian, E. Krasilnikov, S. Lando, and M. Shapiro conjecture that the mean value of the gl-weight system is a tau function of the KP hierarchy.
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Séminaire de géométrie arithmétique
Hurwitz moduli spaces of covers of curves of degree $d$ are classical and well studied objects if one assumes that $d!$ is invertible and hence no wild ramification phenomena occur. There were very few attempts to study the wild case. In the most important one Abramovich and Oort started with the classical space $H_{2,1,0,4}$ of double covers of $P^1$ ramified at four points and (following an idea of Kontsevich and Pandariphande) described its schematic closure $H$ in the space of stable maps over $Z$. The result over $F_2$ was both strange and informative, but lacked a modular interpretation.
In the main part of my talk I will describe the example of Abramovich-Oort and then tell about a work in progress of Hippold, where a (logarithmic) modular version of Hurwitz space of degree $p$ is constructed when only $(p-1)!$ is invertible. In particular, it conceptually explains phenomena observed by Abramovich-Oort. In the second part I will briefly describe another outcome of the same ideas. It was observed by Abramovich-Ollson-Vistoli that $H$ is the blowing up of the modular curve $X(2)$. This is not a coincidence, and the same ideas can be used to refine the wild level structures of Drinfeld and construct modular interpretation of the minimal modifications of the curves $X(p^n)$ which separate ordinary branches at any supersingular point. This is a work in progress and I’ll only indicate the basic idea and some examples. 
 
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The magic triangle due to Cvitanovic and Deligne-Gross is an extension of the Freudenthal-Tits magic square of semisimple Lie algebras. In a recent work with Kimyeong Lee, we identify all 2d rational conformal field theories associated to the magic triangle. These include various Wess-Zumino-Witten models, Virasoro minimal models, compact bosons and their non-diagonal modular invariants. At level one, we find a two-parameter family of modular linear differential equation of fourth order whose solutions produce the affine characters of all elements in the magic triangle. We find a universal coset relation for the whole triangle which generalizes the dual pairs with respect to (E8)_1 in the Cvitanovic-Deligne exceptional series. At level two, we find a special row of the triangle – the subexceptional series has novel N=1 supersymmetry, and the super characters satisfy a one-parameter family of fermionic modular linear differential equations. Moreover, we find many new coset constructions involving WZW models at higher levels.
 
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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 
 
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Seed Seminar of Mathematics and Physics
Winter ’26: Flavors of Amplitudes 
 
 
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Seed Seminar of Mathematics and Physics
Winter ’26: Flavors of Amplitudes 
 
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Seed Seminar of Mathematics and Physics
Winter ’26: Flavors of Amplitudes 
 
 
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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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