Organising Committee: Andrei Negut (Massachussetts Institute of Technology), Francesco Sala (Università di Pisa) and Olivier Schiffmann (CNRS and Université de Paris-Sud)

Scientific Committee: Mina Aganagic (University of California at Berkeley), Hiraku Nakajima (Kavli IPMU), Nikita Nekrasov (Simons Center for Geometry and Physics), and Andrei Okounkov (Colombia University)

The 2021 IHES Summer school on « Enumerative Geometry, Physics and Representation Theory » will be held in a blended format at the Institut des Hautes Etudes Scientifiques (IHES) from 5 to 16 July 2021 with a reduced number of selected participants and through Zoom for all those who are interested in the subject (cf.link to the new registration form below).

This school is open to everybody but intended primarily for young participants, including Ph.D. students and postdoctoral fellows.

The School will be managed via a Slack workspace. If you have registered but you have not received yet the registration link to the Slack workspace, please contact Francesco Sala

The main theme of this Summer School is enumerative geometry, with particular emphasis on connections with mathematical physics and representation theory. As its core, enumerative geometry is about counting geometric objects. The subject has a history of more than 2 000 years and has enjoyed many wonderful breakthroughs in the golden years of classical algebraic geometry, but we will be interested in more recent developments.

This Summer School will focus on the following main subjects:

counting curves and sheaves (Gromov-Witten theory, Donaldson-Thomas and related theories)
gauge theory enumerative geometry (3d gauge theories and Coulomb branches, 4d gauge theories, and Vafa-Witten invariants, etc)
applications of enumerative geometry to categorification and low-dimensional topology
Hall algebras and their refined versions (cohomological, K-theoretic, derived categories)

INVITED LECTURERS:
     Eugene Gorsky (University of California at Davis)
     Joel Kamnitzer (University of Toronto)
     Davesh Maulik (Massachusetts Institute of Technology)
     Rahul Pandharipande (ETH Zürich)
     Markus Reineke (Ruhr-Universität Bochum)
     Richard Thomas (Imperial College London)

ADVANCED TALKS:
     Pierrick Bousseau (CNRS and Université Paris-Saclay)
     Alexander Braverman (University of Toronto and Perimeter Institute for Theoretical Physics)
     Tudor Dimofte (University of California at Davis and University of Edinburgh)
     Lothar Gottsche (ICTP)
     Michael Groechenig (University of Toronto)
     Maxim Kontsevich (IHES)
     Georg Oberdieck (Mathematisches Institut der Universität Bonn)
     Richard Rimanyi (University of North Carolina at Chapel Hill)
     Peng Shan (Tsinghua University)
     Dimitri Zvonkine (Laboratoire Mathématiques de Versailles)

EXERCISE SESSIONS / Q&A SESSIONS:
     For Gorsky’s course: Oscar Kivinen (University of Toronto),  
                                          Jose Simental Rodriguez (Max-Planck Institute for Mathematics).

     For Kamnitzer’s course: Yehao Zhou (Perimeter Institute for Theoretical Physics), 
                                                Michael McBreen (Chinese University of Hong Kong).

     For Maulik’s course: Junliang Shen (Yale University).

     For Thomas’ course: Woonam Lim (ETH Zürich), 
                                           Michail Savvas (University of California, San Diego),
                                           Shubham Sinha (University of California, San Diego).

 

This is an IHES Summer School organized with the support of the Société Générale and in partnership with the Fondation Mathématique Jacques Hadamard, the National Science Foundation, the Clay Mathematics Institute and the Foundation Compositio Mathematica.

In the Heisenberg picture of quantum mechanics, time evolution is a one-parameter family of automorphisms of operator algebra. Restricted to short times the equivalence between time evolution and quantum circuits, especially the property that it maps a local operator to another, has been implanted in theoretical studies of topological phases of matter. In this talk, I will explain recent findings that not all locality-preserving automorphisms, also called quantum cellular automata, can be written as quantum circuits — there exists a « discrete time dynamics » that cannot have a « Hamiltonian. » These are tightly related to static, topological many-body states. I will give results on the classification of these automorphisms, and connect them to locally generated subalgebras in one lower dimension.

Participer à la réunion Zoom
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We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types  of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear luttinger liquid, their structure is more complicated and not understood.

Participer à la réunion Zoom
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The Berry phase is a well-known phenomenon in quantum mechanics with many profound implications. It describes the response of the phase of the wavefunction to the adiabatic evolution of system parameters, defining a U(1) connection on the parameter space. In many-body systems described by quantum field theory, we may also allow the parameters to vary in space, and we find a higher group connection generalizing the Berry phase. This connection also describes phenomena such as the Thouless pump and its generalizations. It allows us to constrain the global structure of phase diagrams by probing non-contractible cycles in the space of quantum field theories. In a typical phase diagram drawn in R^n, these cycles surround topologically-protected critical loci called diabolical points, in analogy to the quantum mechanical singularities which act as « monopoles » for the Berry connection. I will discuss these concepts in more detail, as well as a bulk-boundary correspondence and some recent applications to phase diagrams of topologically ordered systems. This talk is based on https://arxiv.org/abs/2004.10758 w/ Po-Shen Hsin and Anton Kapustin https://arxiv.org/abs/2110.07599 and its sequel, 2110.xxxx w/ Nathanan Tantivasadakarn, Ashvin Vishwanath, and Ruben Verresen.

Participer à la réunion Zoom
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(indiquez vos propres prénom et nom) et laissez le corps du message vide.

 

 

—————————————- APPLICATIONS ARE CLOSED ——————————————

Organizing/Scientific Committee: Emmanuel Breuillard (Univ. of Cambridge), Richard Canary (Univ. Michigan), Indira Chatterji (Univ. Nice-Sophia Antipolis), Fanny Kassel (CNRS-IHES)

The Summer school on « Aspects of Geometric Group Theory » will be held at the Institut des Hautes Etudes Scientifiques (IHES) from 8 to 19 July 2019. IHES is located in Bures-sur-Yvette, south of Paris (40 minutes by train from Paris).

This school is open to everybody but intended primarily for young participants, including PhD students and postdoctoral fellows.

A group is a mathematical object encoding natural notions of symmetries and transformations. Geometric group theory is an area in mathematics devoted to the study of discrete groups by exploring connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act.

As a distinct area, geometric group theory is relatively new, and became an identifiable branch of mathematics in the early 1990s. Geometric group theory closely interacts with low-dimensional topology, hyperbolic geometry, Lie groups and homogeneous spaces, algebraic topology, computational group theory, and differential geometry. There are also substantial connections with complexity theory, mathematical logic, dynamical systems, probability theory, K-theory, and other areas of mathematics.

Nowadays, geometric group theory is a very active and competitive area of research, as shown by the many conferences in the field but also several special programs such as an IHP program in 2014, a jumbo MSRI program in 2016 and a program at the Newton Institute in 2017 to name a few.

We will choose a few important trends in geometric group theory and teach those to graduate students across mathematical fields, so that young people in several areas of mathematics such as algebra, geometry, dynamics, or topology have some basics to either understand a few problems in geometric group theory, or use geometric group theory methods in their respective fields. Geometric group theory is a very broad area, and we will mainly focus on geometric aspects.

INVITED SPEAKERS:

So far the following people have agreed to give a mini-course:

Yves Benoist (CNRS and Université Paris-Sud)
Kai-Uwe Bux (Universität Bielefeld)
Ruth Charney Brandeis University)
François Dahmani (Université Grenoble Alpes)
Anna Erschler (CNRS and ENS)
François Guéritaud (CNRS and Université de Lille)
Kathryn Mann (Brown University)
Yair Minsky (Yale University)
Karen Vogtmann (University of Warwick)
Genevieve Walsh (Tufts University)
Anna Wienhard (Universität Heidelberg)
Daniel T. Wise (McGill University)

This is an IHES Summer School, organized in partnership with the Clay Mathematical Institute, and the support of the Société Générale, the FMJH, the IUF, the ANR GAMME, the project Jeunes Géomètres, the National Science Foundation and the ERC.

 

Organized as part of the IHÉS Lectures, this Summer School aims to provide PhD students, post-docs, and young researchers with an overview of recent developments in the theory of moduli spaces of pseudoholomorphic curves in symplectic and contact geometry.

Moduli spaces of pseudoholomorphic curves arise as the zero set of a Fredholm section of a suitable bundle. Provided this section can be appropriately perturbed, these moduli spaces yield powerful contact and symplectic invariants such as Gromov-Witten theory, contact homology, symplectic homology, and Symplectic Field Theory. Constructions and applications of these invariants will be addressed in detail during the workshop. There are two main perturbative techniques, geometric and functional analytic.

The geometric perturbation methods are powerful for applications and practical from a computational point of view but typically require many restrictive assumptions and fail to generalize broadly. We will introduce researchers to the polyfold machinery of Hofer, Wysocki, and Zehnder, a new analytic framework designed to resolve the issue of transversality systematically. As computations are integral in applications of the aforementioned invariants, we will also explore how geometric perturbation schemes can be incorporated into the polyfold package.

We will supplement 7 mini courses with moderated discussions and related talks by senior faculty on current and future directions for the field.

Confirmed speakers:

M. Abouzaid, Columbia University *
P. Biran, ETH Zürich
N. Bottman, Massachusetts Institute of Technology
F. Bourgeois, Université Paris-Sud Orsay
D. Cristofaro-Gardiner, Harvard University
T. Ekholm, Uppsala University *
Y. Eliashberg, Stanford
J. Fish, Institute for Advanced Study *
H. Hofer, Institute for Advanced Study *
M. Hutchings, UC Berkeley *
D. McDuff, Barnard College, Columbia University
J. Nelson, Columbia University and the Institute for Advanced Study
I. Smith, University of Cambridge
J. Solomon, Hebrew University
C. Viterbo, Ecole Normale Supérieure
K. Wehrheim, UC Berkeley *
C. Wendl, University College London *

* Mini course speakers

Organizing Committee

Chair: J. Nelson (Columbia University and the Institute for Advanced Study)
D. Cristofaro-Gardiner (Harvard University)
J. Fish (Institute for Advanced Study and UMass Boston)

Scientific Advisory Committee

H. Hofer (Institute for Advanced Study)
M. Hutchings (UC Berkeley)
D. McDuff (Barnard College, Columbia University)

With the support of La Société Générale

 

The Summer school on "Spectral properties of large random objects" will be held at the Institut des Hautes Etudes Scientifiques (IHES) from July 17 to July 28, 2017. IHES is located in Bures-sur-Yvette, south of Paris (40 minutes by train from Paris).

The school is open to everybody but intended primarily for young participants, including PhD students and postdoctoral fellows.

Studying spectral properties of large random objects has been a very active playground in probability theory, mathematical physics and computer science during the last decades. 

The motivations are manifold: viewing random matrices as a model for complicated quantum Hamiltonians, studying random Schrödinger operators to understand the Anderson localization phenomenon, viewing eigenvectors of random matrices as models for eigenmodes of quantized chaotic systems, or understanding the geometry of large (random) graphs such as expanders via the spectral properties of their adjacency matrices. In those studies the emphasis is generally put either on the eigenvalues or the eigenvectors of the object.

The goal of the summer school is to present to the selected students (from master students to postdocs) a panoramic view of this rich area, in order to arouse their interest for some old problems which are coming back on stage, as well as the new exciting horizons of the field.

Some funding is available for young participants (more info at the bottom of the page)

Main courses:

• Charles BORDENAVE (Université de Toulouse) 
   Spectrum of random graphs
• Paul BOURGADE (New York University) 
   Universality and quantum unique ergodicity in random matrix theory
• Frédéric KLOPP (Université Pierre et Marie Curie)  
   Large systems of interacting quantum particles in a random field
• Eyal LUBETZKY (New York University) 
   Spectral vs. geometric approaches to random walks on random graphs
• Yuval PERES (Microsoft Research) 
   The cutoff phenomenon and rate of escape for Markov chains
• Christophe SABOT (Université de Lyon 1) 
   Self-interacting processes and random Schrödinger operators
• Balint VIRAG  (University of Toronto) 
  Operator limits of random matrices
• Simone WARZEL  (Technische Universität München)  
   Topics in random operator theory

Talks by:

• Nathanaël ENRIQUEZ (Université Paris X, LPMA)
• Camille MALE (CNRS & Université de Bordeaux)
• Justin SALEZ (Université Paris-Diderot, LPMA)

Organising Committee:

Nicolas CURIEN (Université Paris-Sud) 
Hugo DUMINIL-COPIN (IHES)
Jean-François LE GALL (Université Paris-Sud)
Stéphane NONNENMACHER (Université Paris-Sud)

With the support of

 

Objective

­ ­ Organised as part of the "IHÉS Lectures", this Summer School aims to train PhD students, post-docs and young researchers on recent topics of Analytic Number Theory and to promote exchanges between young researchers of all nationalities.

Analytic number theory began with the first questions concerning the distribution of prime numbers. Since then, the subject has evolved in many directions; it has influenced and interacted with many areas of mathematics, by lending or borrowing ideas going from combinatorics to representation theory, and from modular forms to the deepest reaches of algebraic geometry.

The summer school will cover both classical and emerging topics of analytic number theory, with a focus on the properties of prime numbers:

(1) advanced sieve methods and their refinements, including approaches to gaps between primes and asymptotic sieve for primes;

(2) distribution of arithmetic functions in arithmetic progressions, especially in ranges beyond the direct reach of the Riemann Hypothesis;

(3) exponential sums over finite fields, and their analytic applications, with a focus on the formalism and uses of Frobenius trace functions;

(4) modular forms and associated L-functions, and other analytic aspects of the Langlands program, such as the behavior of torsion homology;

(5) additive combinatorics.

 

­ ­

Avec le soutien de
la Société Générale

 

Speakers

Jean BOURGAIN (Princeton, USA)

Valentin BLOMER (Universität Göttingen, Germany)

Etienne FOUVRY (Université Paris-Sud, Orsay)

Andrew GRANVILLE (Université de Montréal, Québec)

Harald HELFGOTT (ENS, Paris)

Henryk IWANIEC (Rutgers University, Piscataway, USA)

Emmanuel KOWALSKI (ETH Zürich, Switzerland)

Philippe MICHEL (EPFL Lausanne, Switzerland)

Peter SARNAK (IAS Princeton, USA)

Kannan SOUNDARARAJAN (Stanford University, USA)

Terence TAO (UCLA, USA)

Akshay VENKATESH (Stanford University, USA)

Autre événement

Workshop on Analytic Number Theory and Geometry
organisé par Farrell Brumley
24-25 juillet, 2014
Université Paris 13

Organising Committee Elli Pomoni(DESY)  Bruno Le Floch (Princeton University) and Masahito Yamazaki (Kavli IPMU, University of Tokyo)

Scientific Committee: Vasily Pestun (IHES), Silviu Pufu (Princeton University), Joerg Teschner (DESY)

The Summer school on "Supersymmetric Localization and Exact Results" will be held at the Institut des Hautes Etudes Scientifiques (IHES) from July 16 to July 27, 2018. IHES is located in Bures-sur-Yvette, south of Paris (40 minutes by train from Paris).

This school is open to everybody but intended primarily for young participants, including PhD students and postdoctoral fellows.

Significant progress has been made in the study of gauge theories in the last decade. Thanks to the discovery of novel techniques and especially supersymmetric localization, the field now possesses a plethora of exact results that previously seemed unreachable.

Starting with the work of Nekrasov who computed the instanton partition function for N=2 theories in four dimensions, Pestun computed the exact partition function on a four-sphere for theories with N=2 supersymmetry. Shortly after the partition functions as well as other observables in various spacetime dimensions and compact manifolds were computed.

Our school aims in deepening the understanding of current results and at investigating which of our current methods are transferable to theories with less supersymmetry, as well as trying to increase the list of possible observables that are computable via localization.

Each week will feature three or four speakers giving one lecture per day. During the first week, in addition to these three one hour and a half lectures there will be discussion and homework sessions in the afternoon. During the second week, some of the lectures will be replaced by talks on more advanced topics.

The main lectures will cover the following topics:

Week 1: Introduction to localization, Localization of instantons and Exact results on 4d N=2 theories

Week 2:  Topological strings and matrix models, M5 brane compactifications and Zamolodchikov metric and tt^* equation

Advanced talks week 2: Chiral algebras, N=1 localization, Localization with boundaries, line operators, surface operators, relations to CFT and integrable systems

INVITED SPEAKERS:

Week 1: 1h30 per topic per day
     Francesco Benini(SISSA
     Guido Festuccia (Uppsala)
     Wolfger Peelaers(Rutgers)

Advanced talk in week 1: 2-3 hours
     Seiji Terashima (Kyoto)

Week 2: 1h30 per topic per day
     Zohar Komargodski (Stony Brook)
     Maxim Zabzine (Uppsala)

Advanced talks in the second week: 2-3 hours each
     Nikita Nekrasov (Simons Center)
     Takuya Okuda (Tokyo)
     Balt van Rees (Durham)
 

Some funding is available for young participants (more info at the bottom of the page)

With the support of

 

Organized as part of the IHÉS Lectures, this 2-weeks Summer School will be the last major scientific event of the special trimester on Non-Linear Waves that will start in the beginning of May 2016 at IHÉS. This school aims at providing an overview of recent developments in the field at this stage of the new cycle started a few years ago and to provide to post-docs and researchers in the early stage of their career working in these domains an opportunity to interact with leading experts on the subject.

Another objective is to gather researchers with different backgrounds whose research is much more converging today than 4 years ago, such as the French schools working on fluid models, on kinetic theory, dynamical systems and partial differential equations in relation to finite-dimensional Hamiltonian models or the microlocal community.

Last but not least, another objective would be the following: the advances have helped to solve classical problems from physics with new and very advanced methods based on analytical intuition thus not always understood or simply not well-known by the physicists. The idea would be to initiate a transfer to physicists interested in non linear waves phenomena and intensify the discussions on more realistic models, whether fluid, kinetic or of high-frequency waves.

We will supplement mini courses (3 hours) in the morning and plenary talks in the afternoon (40-45 minutes) during 2 weeks.

Mini course speakers:

Rupert FRANK (California Institute of Technology)
Carlos KENIG (University of Chicago)
Nader MASMOUDI (Courant Institute of Mathematical Sciences)
Benoît PAUSADER (Brown University)
Michela PROCESI (Universita di Roma 1)
Robert STRAIN (University of Pennsylvania)
Daniel TATARU (University of California at Berkeley)

Plenary talks speakers:

Stefano BIANCHINI (SISSA)
Rémi CARLES (CNRS – IMAG Montpellier)
Stephen GUSTAFSON (University of British Columbia)
Joachim KRIEGER (EPFL)
Hans LINDBLAD  (Johns Hopkins University)
Hiroshi MATANO  (School of Science, University of Tokyo)
Natasa  PAVLOVIC (University of Texas at Austin)
Robert PEGO  (Carnegie Mellon University)
Svetlana ROUDENKO (George Washington University)
Gigliola  STAFFILANI (Massachusetts Institute of Technology)
Tai-Peng TSAI (University of British Columbia)
Nicola VISCIGLIA (Universita di Pisa)
Sijue WU (University of Michigan)

Organising Committee:

Yvan MARTEL (École Polytechnique)
Frank MERLE (Université de Cergy-Pontoise & IHÉS)
Fabrice PLANCHON (Université Nice Sophia-Antipolis)
 

Crédit photographique: © CNRS Photothèque
RAJAU Benoît (UMR7538 – Laboratoire de physique des lasers (LPL), VILLETANEUSE et VRIGNAUD François (UMR6172 – XLIM – LIMOGES)

With the support of

Surprisingly, there exist connected components of character varieties of fundamental groups of surfaces in semisimple Lie groups consisting only of injective representations with discrete image. Guichard and Wienhard introduced the notion of Θ-positive representations as a conjectural framework to explain this phenomenon. I will discuss joint work with Jonas Beyrer in which we establish several geometric properties of Θ-positive representations in PO(p,q). As an application, we deduce that they indeed form connected components of character varieties.

==================================================================

IHES Covid-19 regulations:

– all the participants who will attend the event in person will have to keep their mask on in indoor spaces
and where the social distancing is not possible;
– speakers will be free to wear their mask or not at the moment of their talk if they feel more comfortable
without it;
– Up to 25 persons in the conference room, every participant will be asked to be able to provide a health pass
– Over 25 persons in the conference room, every participant will be asked to provide a health pass which will
be checked at the entrance of the conference room.

==================================================================

Emergence is a major buzz word of our times. My working definition, which gives plenty of room for manoeuvre is: the appearance of many body phenomena of higher symmetry than that of the Hamiltonian and degrees of freedom at the microscopic level.

In this colloquium I will discuss a topical example – the frustrated magnetic material, spin ice. Here, to an excellent approximation a classical field theoretic description with continuous U(1) symmetry emerges from Ising like degrees of freedom. The associated quasi-particles appear to be freely moving magnetic charge – magnetic monopoles – and the system behaves as a magnetic Coulomb fluid in the grand canonical ensemble with intrinsic topological properties. With the addition of quantum fluctuations the emergent magneto-statics develops further into a complete analogue of quantum electrodynamics. I will aliment this discussion with experimental results from a wide range of systems.

https://us02web.zoom.us/j/85270888147?pwd=aXdOVXBTSmNEU00vVFE2bXhqdE5vdz09

ID de réunion : 852 7088 8147
Code secret : 276852