Combinatorics an Arithmetic for Physics: special days

The meeting’s focus is on questions of discrete mathematics and number theory with an emphasis on computability. Problems are drawn mainly from theoretical physics (renormalisation, combinatorial physics, geometry) or related to its models. Computation, based on combinatorial structures (graphs, trees, words, automata, semirings, bases) or classic structures (operators, Hopf algebras, evolution equations, special functions, categories) are good candidates for computer-based implantation and experimentation.

Organised by : Gérard H.E. Duchamp, Maxim Kontsevitch, Gleb Koshevoy et Hoang Ngoc Minh

Invited speakers :

Nicolas Behr (IRIF Université Paris Diderot)
Alin Bostan (INRIA Saclay)
Marek Bozejko (University of Wroclaw)
Pierre Cartier (IHES)
Gérard Duchamp (IHP & Paris 13)
Dimitri Grigoryev (CNRS-Lille 1)
Dmitry Gurevich (Université de Valenciennes)
Natalia Iyudu (University of Edinburgh & IHES)
Richard Kerner (LPTMC)
Gleb Koshevoy (Poncelet Lab., Moscow)
Hoang Ngoc Minh (Lille 2 & LIPN)
Karol Penson (LPTMC & Paris 6)
Pierre Vanhove (CEA/Saclay)

      

Combinatorics an Arithmetic for Physics: special days

 

Organised by : Gérard H.E. Duchamp, Maxim Kontsevitch, Gleb Koshevoy et Hoang Ngoc Minh

Invited speakers :

Nicolas Behr (IRIF Université Paris Diderot)
Marek Bozejko (University of Wroclaw)
Pierre Cartier (IHES)
Gérard Duchamp (IHP & Paris 13)
Vladimir Fock (Strasbourg)
Dimitri Grigoryev (CNRS-Lille 1)
Gleb Koshevoy (Poncelet Lab., Moscow)
Pierre Lairez (INRIA-LIX)
Hoang Ngoc Minh (Lille 2 & LIPN)
Karol Penson (LPTMC & Paris 6)
Leila Schneps (CNRS-Paris 6)

      

Jointly organised by :
the Institut des Hautes Études Scientifiques and the Agence Nationale de la Recherche

Thursday 12 January 2012

­­

 Scientific Organisers
Ahmed Abbes (CNRS, IHÉS), Christophe Breuil (CNRS, Université Paris-Sud)­

­Programme­

­­­­­­ ­ ­

9h30-10h15
Welcome of the partipants 

10h15-11h15
T. Gee (Imperial College London)
New perspectives on the Breuil-Mézard conjecture (joint with M. Emerton)

11h30-12h30
F. Andreatta (Università di Milano)
Families of p-adic overconvergent modular forms

12h30-14h
Lunch break 
 

14h-15h
B. Schraen (CNRS et Université de Versailles)
Quelques propriétés des représentations mod p de GL2(F)

15h15-16h
M. Gros ­(CNRS et Université de Rennes 1) 
Une correspondance de Simpson p-adique, I : aspects locaux

16h -16h30
Coffee Break
 

16h30-17h15
A. Abbes (CNRS et IHÉS)
Une correspondance de Simpson p-adique, II : aspects globaux

­

 

.       

Watch the videos on Youtube.

—————————————– IMPORTANT INFORMATION ——————————————

>> Due to the Covid-19 pandemic, the 2020 Summer School has been organised through zoom. Mini-courses and talks have been recorded and downloaded on the IHES YouTube Channel.

Organising Committee: Aravind Asok (University of Southern California), Frédéric Déglise (CNRS Dijon), Grigory Garkusha (Swansea University), Paul Arne Østvær (University of Oslo)

Scientific Committee: Eric M. Friedlander (University of Southern California), Haynes R. Miller (MIT Department of Mathematics), Bertrand Toën (CNRS Toulouse)

The IHES 2020 Summer School on « Motivic, Equivariant and Non-commutative Homotopy Theory » will be held from 6 to 17 July 2020.

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

The IHES 2020 Summer School will focus on topics in motivic and equivariant homotopy theory, and non-commutative geometry.

These three subjects are currently experiencing a phase of intense growth and development:

long-standing central conjectures have been solved;
existing theories are being perfected;
many new foundational developments are being made on this basis.

It’s expected that these developments will spur many further advances and interactions in the near future.

The lecture series and research talks at the IHES Summer School will focus on presenting the latest developments in topics related to categories of motives, calculational and foundational aspects of motivic and equivariant homotopy theory, and the generalisations of these tools and techniques in the setting of non-commutative geometry.

INVITED SPEAKERS

The Summer School will feature mini-courses by

*  Clark Barwick (University of Edinburgh)
*  Teena Gerhardt (Michigan State University)
*  Daniel Isaksen (Wayne State University)
*  Dmitry Kaledin (Steklov Mathematical Inst. & National Research Univ. Higher School of Economics)
*  Marc Levine (Universität Duisburg-Essen)
*  Ivan Panin (St. Petersburg Department of Mathematics)
*  Goncalo Tabuada (MIT/University of Warwick)

as well as research talks by

*  Federico Binda (University of Milan)
*  Tom Bachmann (MIT)
*  Mike Hill (UCLA)
*  Geoffroy Horel (University Paris 13)
*  Alexander Neshitov (Western University)
*  Angélica M. Osorno (Reed College)
*  Marco Robalo (Institut de Mathématiques de Jussieu)
*  Kirsten Wickelgren (Duke University)

 

Both the lecture series and research talks will focus on presenting the latest developments in topics related to categories of motives, calculational and foundational aspects of motivic and equivariant homotopy theory, and the generalisations of these tools and techniques in the setting of non-commutative geometry.

This is an IHES Summer School organised in partnership with the Research Council of Norway, the Fondation Mathématique Jacques Hadamard and the ANR, and the support of the Société Générale and the ERC.

 

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
https://us02web.zoom.us/j/83786264059?pwd=Nk81UDhlT3JLSDFkd29KY0NUMFYvZz09

ID de réunion : 837 8626 4059
Code secret : 051224

Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe quantum_encounters_seminar PRENOM NOM »
(indiquez vos propres prénom et nom) et laissez le corps du message vide.

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
https://us02web.zoom.us/j/82078858054?pwd=KzhaZldTbFhJclUrK3YrYkI5VTJVdz09

ID de réunion : 820 7885 8054
Code secret : 560193

Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe quantum_encounters_seminar PRENOM NOM »
(indiquez vos propres prénom et nom) et laissez le corps du message vide.

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
https://us02web.zoom.us/j/87445066109?pwd=U1Bjc211enZlOGFYd0l5REltRWVqQT09

ID de réunion : 874 4506 6109
Code secret : 812780

Pour être informé des prochains séminaires vous pouvez vous abonner à la liste de diffusion en écrivant un mail à sympa@listes.math.cnrs.fr avec comme sujet: « subscribe quantum_encounters_seminar PRENOM NOM »
(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