In 1970 Matiyasevich, building on earlier work of Davis–Putnam–Robinson, proved that every enumerable subset of $mathbb{Z}$ is Diophantine, thus showing that Hilbert’s 10th problem is undecidable for $mathbb{Z}$. The problem of extending this result to the ring of integers of number fields (and more generally to finitely generated infinite rings) has attracted significant attention and, thanks to the efforts of many mathematicians, the task has been reduced to the problem of constructing, for certain quadratic extensions of number fields $L/K$, an elliptic curve $E/K$ with $rk(E(L))=rk(E(K))>0$.  In this talk I will explain joint work with Peter Koymans, where we use Green–Tao to construct the desired elliptic curves, settling Hilbert 10 for every finitely generated infinite ring.
 
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Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Atttention : La première Leçon aura lieu à l’IMO, Amphithéâtre Yoccoz, le 11 mars de 10h à 12h
Retrouvez toutes ces informations sur le site de la Fondation Mathématique Jacques Hadamard :
https://www.fondation-hadamard.fr/fr/evenements/cours-avances/
Abstract:
We will discuss some recent work around the geometric Langlands program. Specific topics will depend on audience interest, but I hope to introduce the subject generally, discuss some parts of the proof of geometric Langlands in characteristic 0, give partial results in characteristic p, and discuss some arithmetic applications.
 

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
In the first part of my talk, I will discuss the distinction between (i) the conservativeenergy, which is conserved under the conservative equations of motion, and (ii) the binding energy, which enters the flux-balance laws. The difference between these two energies is called a Schott term and was historically expected to vanish for circular orbits. But I will show that at 4PN, the Schott term does not vanish due to a hereditary piece in the dissipative equations of motion. I will explain how the Schott term can link the notions of orbital and waveform frequencies and properly ensure the absence of arbitrary constants in physical observables within the post-Newtonian formalism.
In the second part of my talk, I will present the derivation of the action-angle 4PN conservative Hamiltonian for bound eccentric systems, including the 4PN tail term. The latter appears as an enhancement function of the eccentricity, which takes the form of a well-controlled infinite sum, which is resummed in a simple form such as to maintain a 10-5 relative accuracy for any eccentricity. It is then immediate to deduce the 4PN links between the conservative constants of motion (energy and angular momentum) and the fundamental (radial and azimuthal) orbital frequencies. From there, I obtain the 4PN redshift, which is in perfect agreement with analytical self-force.
 
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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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