Séminaire de géométrie arithmétique
The hard Lefschetz theorem and Hodge-Riemann relations are fundamental results on the cohomology of Kähler manifolds and have found important applications in combinatorics. In this talk, we will explore extensions of Hodge-Riemann relations to certain vector bundles and applications to log-concavity.
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Phases of matter and the transitions between them are famously characterized within the Landau paradigm and Landau–Ginzburg theory: phases are labeled by broken or unbroken symmetries, while phase transitions are described in terms of scalar order parameters. There are, however, phases beyond the standard Landau paradigm that are distinguished not by the realization of ordinary symmetries, but by that of generalized global symmetries. Among these, topologically ordered phases in (2+1)d possess non-invertible 1-form symmetries described by anyon lines. In this talk, I will present a framework for describing transitions between topologically ordered phases related by anyon proliferation, which can be viewed as a non-invertible generalization of the choice of the unbroken symmetry. The resulting theories involve scalar fields coupled to gauge fields. A crucial ingredient in this construction is the (3+1)d Symmetry Topological Field Theory (SymTFT), which allows to separate symmetry from dynamics and will be employed in a rather unconventional way.
 
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In this talk I will discuss an attempt of unifying under a simple geometric picture, the plethora of crossing symmetric dispersion relations existing in literature.
Each dispersion is valid on a different finite window in energy, but none of them could be extended to infinity.
I will explain how they can all be understood from a simple choice of a foliation of the kinematics space. 
This geometric viewpoint also suggests the existence of a particular (but not so nice) foliation that naturally covers all energies. Unfortunately, this example turns out to be impractical for phenomenological and bootstrap applications. I will comment why, and what teaches us about the dual bootstrap.
 
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In this series of lectures, I will introduce the « fuzzy (non-commutative) sphere regularization, » a recently proposed non-perturbative approach to 3D CFTs. I will first elucidate its fundamental concepts and then dive into illustrative examples, including the 3D Ising transition, fermionic CFTs, and Chern-Simons matter theories. I will comment on the potential theoretical direction in understanding fuzzy sphere regularization from the aspect of algebra on fuzzy sphere.

In this series of lectures, I will introduce the « fuzzy (non-commutative) sphere regularization, » a recently proposed non-perturbative approach to 3D CFTs. I will first elucidate its fundamental concepts and then dive into illustrative examples, including the 3D Ising transition, fermionic CFTs, and Chern-Simons matter theories. I will comment on the potential theoretical direction in understanding fuzzy sphere regularization from the aspect of algebra on fuzzy sphere.

In this series of lectures, I will introduce the « fuzzy (non-commutative) sphere regularization, » a recently proposed non-perturbative approach to 3D CFTs. I will first elucidate its fundamental concepts and then dive into illustrative examples, including the 3D Ising transition, fermionic CFTs, and Chern-Simons matter theories. I will comment on the potential theoretical direction in understanding fuzzy sphere regularization from the aspect of algebra on fuzzy sphere.

In this series of lectures, I will introduce the « fuzzy (non-commutative) sphere regularization, » a recently proposed non-perturbative approach to 3D CFTs. I will first elucidate its fundamental concepts and then dive into illustrative examples, including the 3D Ising transition, fermionic CFTs, and Chern-Simons matter theories. I will comment on the potential theoretical direction in understanding fuzzy sphere regularization from the aspect of algebra on fuzzy sphere.

The Wilson–Fisher (WF) fixed point, a scalar field theory with a quartic interaction in $d = 4 – epsilon$ dimensions, is the textbook example of a weakly coupled CFT. The epsilon expansion accurately reproduces the critical exponents of the $d = 3$ and the $d = 2$ Ising model. This has led to the common view that WF defines a continuous family of CFTs in non-integer dimensions, interpolating between the free theory at $d=4$ and the Ising model at $d = 3$ and $d = 2$. In this talk I will look at what happens to the WF CFT when the number of dimensions approaches an integer value. Identifying the $dto 2$ limit of WF as the $2d$ Ising CFT raises some issues, related to the fact that the $d=2$ CFT has infinitely many conserved currents that the $d>2$ theory does not have. I will propose a scenario, inspired by some exactly solved two-dimensional models, where the $dto 2$ limit of WF contains the $d=2$ Ising CFT as a subsector, but contains more operators which do not completely decouple from the Ising subsector. I will explain why this makes the task of obtaining a $d= 2 + epsilon$ expansion for the Ising model harder.
 
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Motivated by nuclear experiments where a few neutrons are produced by a local source, we develop a formalism of « nonrelativistic conformal collider physics. » We define detector operators in the nonrelativistic conformal field theory describing fermions at unitarity. We reduce the problem of computing the momentum distribution and correlation between final particles produced by a local source (« point-produced ») to the computation of correlation functions involving the detector operators. The general formalism is applied to the point production of three unitary fermions, where we find the momentum and angular distribution of final particles, and point production of a large number of fermions. We discuss a nonrelativistic version of celestial holography, which maps the asymptotic out-state to a quantum wave function in the so-called « oscillator frame. » Based on arXiv:2608.18202 with Cyuan-Han Chang, Subham Dutta Chowdhury, and Ian Moult.
 
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Korea-France Joint Workshop on String Theory    
September 15-18, 2026    at IHES – Marilyn and James Simons Conference Center
Registration deadline (required) : September 10, 2026    
How to get to IHES

 
This workshop will bring together experts in string theory and quantum field theory to discuss recent advances in these fields, and also to foster collaboration between the Korean and French theoretical and mathematical physics communities.
Key topics will include conformal field theory, generalized symmetries and topological quantum field theory, scattering amplitudes, quantum gravity/holography, black-hole physics.
The event will mark the second edition of a new biennial series, alternating between the Korea Institute for Advanced Study (KIAS) and institutions in the Saclay region, near Paris, and it will feature speakers both from Saclay and Korea, as well as worldwide experts in these areas. 

Organizing Committee:
Piljin Yi (KIAS), Sangmin Lee (KIAS), Sungjay Lee (KIAS), Ruben Minasian (IPhT, CEA Saclay), Julio Parra Martinez (IHES), Eric Perlmutter (IPhT, CEA Saclay).
Invited speakers:

Stefano de Angelis (IPhT, CEA Saclay)

Jan de Boer (Univ. of Amsterdam)

Anna Biggs (Princeton Univ.)

Thibault Damour (IHES)

Matilda Delgado (Harvard Univ. & MPI Munich)

Anatoly Dymarsky (University of Kentucky)

Dongmin Gang (Seoul National Univ.)

Elliott Gesteau (MIT & Harvard CMSA)

Rajesh Gopakumar (ICTS, Bangalore)

Mariana Graña (IPhT, CEA Saclay)

Robin Karlsson (Oxford Univ.)

Anton Kapustin (Caltech & IHES)

Jung-Wook Kim (CERN)

Seung-Joo Lee (Yonsei Univ.)

Hong Liu (MIT)

Shiraz Minwalla (TIFR Mumbai)

Mukund Rangamani (QMAP, UC Davis)

Diandian Wang (Harvard Univ.)

Anna Wolz (UCLA)

Alberto Zaffaroni (Milano Bicocca Univ.)

 
Sponsors & Partners:

The 2026 edition of the LSC Meeting, “Breakpoints across Biological Systems”, aims to discuss how instabilities arise and what are the causes of breakpoints at different scales in biological systems (including at the level of cultural evolution in human societies). This topic is heavily influenced by the prospects the entire planet and mankind are facing in front of a rapidly changing environment. Taking the topic in a broader sense, examples of breakpoints that we will discuss include, but are not limited to, pathological events like those observed in heart failure or ecological and social ones when biological niches and societies collapse, but will also include creative or physiological catastrophe events, such as those observed at the root of major evolutionary transitions or in many developmental processes.The scope of this in-person 4 day-long meeting is to bring together scientists from the LSC Committee with invited experts and the IHES scientists to present the latest progress in understanding breakpoints as a multifaceted concept and its many implications on different aspects of life and thus fueling discussions, brainstorm and explore alternative paths towards a better understanding of this concept. The first day will focus particularly on the heart: cardiac death, arrhythmias, and fibrosis patterns.
Stay in touch by subscribing to our mailing list.
 
CARDIO DAY (June 22nd):
Speakers:

Olivier Bernus, Mechanisms underlying Cardiac Arrhythmias, University of Bordeaux & IHU Liryc
Michel Haïssaguerre, Abnormalities of Heart Rhythm, Hôpital Cardiologique du Haut–Lévèque

Discussants:
 

Guillaume Coutance, Heart Failure and Heart Transplant, Assistance Publique Hôpitaux de Paris
Guillaume Fleury, Cardiovascular Pathologies, American Hospital of Paris
Alexander Panfilov, Cardiac Modelling, Ghent University
Hans Dierckx, Cardiac Arrhytmais, Leiden University Medical Center (NL)

 
GENERAL MEETING Speakers:

Uri Alon, Design Principles in Biology, Weizmann Institute of Science
Nathalie Balaban, Antibiotic Resistance, The Hebrew University in Jerusalem
Daniel Kondor, Social Complexity & Collapse, Complexity Science Hub
Athanasios Litsios, Functional Genomics, University of Toronto
Jenny Reddish, Social Complexity & Collapse, Complexity Science Hub
Manuel Thery, Cytoskeleton and Morphogenesis, CEA / ESPCI, Institut Pierre-Gilles de Gennes

 
More details in the Profiles sections.
 
ORGANIZERS:

Yves Barral (ETH Zurich)
Mikhail Gromov (IHES/U. Paris-Saclay & NYU)
Bob Penner (IHES/U. Paris-Saclay & UCLA)
Eugene Koonin (NIH)
Yann LeCun (AMI Labs & NYU)
Nicolas Minc (U. Paris Cité/CNRS)
Pierre-Yves Oudeyer (INRIA Bordeaux)
Yukiko Yamashita (MIT)

EXECUTIVE ORGANIZATION: Grazia Gonella, ETH ZurichCONTACT: lsc@biol.ethz.ch

An origami torus is a piecewise affine isometric embedding of a flat torus into R3. It is surprising that these things exist, but thanks to the work of Burago and Zalgaller in 1960 they do. 30 years later, B&Z proved that every flat torus is realized as an origami torus. In 2023, Lazarus and Tallerie proved that you can realize all flat tori using a single underlying triangulation with about 2500 vertices.
The question remained: how many vertices do you need to make an origami torus? In this talk I will prove that the minimum number of vertices needed is 8. I will also discuss joint work, with Peter Doyle, proving that almost every flat torus is represented by an 8-vertex origami torus. Finally, I will explain work-in-progress with Doyle, Fabian Lander, and Steve Trettel, which shows that in fact every flat torus is represented by an 8-vertex origami torus. If I have time, I will also discuss hyperbolic versions of this business.