The purpose of this course is to propose new foundations for analytic geometry.  The topics covered are as follows: 1. Light condensed abelian groups. 2. Analytic rings.  3. Analytic stacks. 4. Examples.Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire :https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09Code secret : 069444Ce cours sera donné par Dustin Clausen (IHES) conjointement avec Peter Scholze (MPIM Bonn). D.C. donnera ses cours en présentiel les mercredis dans l’amphi Léon Motchane et P.S. donnera ses cours, à partir de Bonn, les vendredis, avec une diffusion zoom dans l’amphi Léon Motchane. Exceptionnellement P.S. donnera les 6 cours du 20 octobre au 10 novembre. 

The purpose of this course is to propose new foundations for analytic geometry.  The topics covered are as follows: 1. Light condensed abelian groups. 2. Analytic rings.  3. Analytic stacks. 4. Examples.Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire :https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09Code secret : 069444Ce cours sera donné par Dustin Clausen (IHES) conjointement avec Peter Scholze (MPIM Bonn). D.C. donnera ses cours en présentiel les mercredis dans l’amphi Léon Motchane et P.S. donnera ses cours, à partir de Bonn, les vendredis, avec une diffusion zoom dans l’amphi Léon Motchane. Exceptionnellement P.S. donnera les 6 cours du 20 octobre au 10 novembre. 

The purpose of this course is to propose new foundations for analytic geometry.  The topics covered are as follows: 1. Light condensed abelian groups. 2. Analytic rings.  3. Analytic stacks. 4. Examples.Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire :https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09Code secret : 069444Ce cours sera donné par Dustin Clausen (IHES) conjointement avec Peter Scholze (MPIM Bonn). D.C. donnera ses cours en présentiel les mercredis dans l’amphi Léon Motchane et P.S. donnera ses cours, à partir de Bonn, les vendredis, avec une diffusion zoom dans l’amphi Léon Motchane. Exceptionnellement P.S. donnera les 6 cours du 20 octobre au 10 novembre. 

The purpose of this course is to propose new foundations for analytic geometry.  The topics covered are as follows: 1. Light condensed abelian groups. 2. Analytic rings.  3. Analytic stacks. 4. Examples.Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire :https://us02web.zoom.us/j/82757036342?pwd=VVUxbHgrWU5VelpQdUlCaHdMOG9Qdz09Code secret : 069444Ce cours sera donné par Dustin Clausen (IHES) conjointement avec Peter Scholze (MPIM Bonn). D.C. donnera ses cours en présentiel les mercredis dans l’amphi Léon Motchane et P.S. donnera ses cours, à partir de Bonn, les vendredis, avec une diffusion zoom dans l’amphi Léon Motchane. Exceptionnellement P.S. donnera les 6 cours du 20 octobre au 10 novembre. 

Gromov-Witten invariants of a smooth projective variety give an infinite tower of cohomology classes on powers of the original variety, satisfying a beautiful system of constraints encoded in the notion of quantum connection.Recently Hiroshi Iritani proved a result controlling the quantum connection of the blowup along a smooth center.The goal of the course is to introduce a new class of birational invariants based on Iritani’s theorem.In particular, one can almost effortlessly prove the non-rationality of a generic cubic 4-fold. Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire : https://us02web.zoom.us/j/89102061199?pwd=TmwzNDRwYzN0Z0JjRzU3aEJETzk5QT09 Code secret : 641368 

Gromov-Witten invariants of a smooth projective variety give an infinite tower of cohomology classes on powers of the original variety, satisfying a beautiful system of constraints encoded in the notion of quantum connection.Recently Hiroshi Iritani proved a result controlling the quantum connection of the blowup along a smooth center.The goal of the course is to introduce a new class of birational invariants based on Iritani’s theorem.In particular, one can almost effortlessly prove the non-rationality of a generic cubic 4-fold.Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire : https://us02web.zoom.us/j/89102061199?pwd=TmwzNDRwYzN0Z0JjRzU3aEJETzk5QT09 Code secret : 641368 

Gromov-Witten invariants of a smooth projective variety give an infinite tower of cohomology classes on powers of the original variety, satisfying a beautiful system of constraints encoded in the notion of quantum connection.Recently Hiroshi Iritani proved a result controlling the quantum connection of the blowup along a smooth center.The goal of the course is to introduce a new class of birational invariants based on Iritani’s theorem.In particular, one can almost effortlessly prove the non-rationality of a generic cubic 4-fold.Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire : https://us02web.zoom.us/j/89102061199?pwd=TmwzNDRwYzN0Z0JjRzU3aEJETzk5QT09 Code secret : 641368 

Gromov-Witten invariants of a smooth projective variety give an infinite tower of cohomology classes on powers of the original variety, satisfying a beautiful system of constraints encoded in the notion of quantum connection.Recently Hiroshi Iritani proved a result controlling the quantum connection of the blowup along a smooth center.The goal of the course is to introduce a new class of birational invariants based on Iritani’s theorem.In particular, one can almost effortlessly prove the non-rationality of a generic cubic 4-fold.Veuillez cliquer sur le lien ci-dessous afin de rejoindre le webinaire : https://us02web.zoom.us/j/89102061199?pwd=TmwzNDRwYzN0Z0JjRzU3aEJETzk5QT09 Code secret : 641368 

Arithmetic Algebraic GeometryJan Nekovář was a mathematician who worked and has made many significant and seminal contributions to algebraic geometry. He left us prematurely in November 2022. Here is a tribute note (in French) by Pierre Colmez.In his memory, Anna Cadoret, IMJ-PRG, Wiesława Nizioł, IMJ-PRG, and Sarah Zerbes, ETH Zürich, organize a conference in arithmetic algebraic geometry at IHES from October 9th to 13th, 2023.This is an international conference in arithmetic geometry, aimed at covering some of the most recent advances in the field with a focus on the areas Jan Nekovář was interested in. Invited Speakers:Tomoyuki Abe, IPMU – University of Tokyo  Spencer Bloch, University of Chicago  Ana Caraiani, Imperial College London – University of BonnHenri  Darmon, McGill University  Vesselin Dimitrov, Institute for Advanced Studies  Matthew  Emerton, University of Chicago  Veronika  Ertl, Universitat Regensburg  Hélène Esnault, Frei Universität Berlin  Olivier Fouquet, Université de Franche-Comté Alexander Goncharov, Yale University  Giada Grossi, CNRS, Université Sorbonne Paris Nord      Jie Lin, Universität Duisburg-Essen  David  Loeffler, University of Warwick   Akhil Mathew, University of Chicago   James Newton, University of Oxford  Alexander Petrov, Harvard University  Alena Pirutka, New York University  Tony Scholl, University of Cambridge   Yunqing Tang, University of California – Berkeley  Jacob Tsimerman, University of Toronto    IHES thanks all the donors of the 2021 Friends of IHES Gala for making this conference possible.

We propose using smeared boundary states as variational approximations to the ground state of a conformal field theory deformed by relevant bulk operators. This is motivated by recent studies of quantum quenches in CFTs and of the entanglement spectrum in massive theories. It gives a simple criterion for choosing which boundary state should correspond to which combination of bulk operators, and leads to a rudimentary phase diagram of the theory in the vicinity of the RG fixed point corresponding to the CFT, as well as rigorous upper bounds on the universal amplitude of the free energy. In the case of the 2d minimal models explicit formulae are available. As a side result we show that the matrix elements of bulk operators between smeared Ishibashi states are simply given by the fusion rules of the CFT. 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 seminaire_physique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

I will explain why positive representations of fundamental groups of surfaces satisfy a « collar lemma » similar to the classical collar lemma for hyperbolic geometry, and have associated positive cross-ratios. As a consequence, I will deduce that positive representations form closed subsets of the representation variety. I will spend some time recalling what a positive representation is, what the associated cross-ratios are, and explain the main new object that we shall use and that we call « photons ». This is joint work with Jonas Beyrer, Olivier Guichard, Beatrice Pozzetti and Anna Wienhard.

Quantum representations are families of finite-dimensional representations of mapping class groups satisfying strong compatibility conditions. One of the most well-known (the so-called SO(3)-TQFT) depends on a parameter q which is a root of unity of order 2r (r odd). These representations preserve a Hermitian form: recently, with B. Deroin, we explained how to compute its signature (among other things). More recently, I observed that this computation is related to the trace field of the 2-bridge knot K(r,s) where q=exp(iπs/r). During the talk, I will explain this relation and the objects involved in it.