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.

Assume certain comparison between non-commutative Hodge structures and classical Hodge structures, we show the categorical enumerative invariants associated with a smooth projective family of Calabi-Yau 3-folds satisfy the holomorphic anomaly equations. This naturally leads to the study of geometric structures on moduli spaces of smooth projective Calabi-Yau 3-folds. ========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_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

For certain problems, taking the Borel sum of an intuitively chosen divergent series solution will often produce a holomorphic solution. When does this happen, and what is special about the holomorphic solutions obtained in this way? We will present work in progress on these questions, focusing on two kinds of problems: linear ODEs and integrals over Lefschetz thimbles.Day IIThe second day’s lectures are dedicated to a family of examples: the Airy-Lucas functions introduced by Charbonnier et al. (arXiv:2203.16523). These functions satisfy linear ODEs that generalize the Airy equation. They can also, like the Airy function, be expressed as thimble integrals. We will explain, from both perspectives, why these solutions can be obtained by Borel summation.We will conclude by describing general classes of linear ODEs and 1d thimble integrals that can be analyzed in the same way. ========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_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

For certain problems, taking the Borel sum of an intuitively chosen divergent series solution will often produce a holomorphic solution. When does this happen, and what is special about the holomorphic solutions obtained in this way? We will present work in progress on these questions, focusing on two kinds of problems: linear ODEs and integrals over Lefschetz thimbles.Day IWe will start the first day’s lectures with a presentation of our questions and an overview of our expected results.Next, we will review the Laplace and Borel transforms from a new perspective that highlights the geometric structure of the Borel plane. This geometric structure is relevant to both of the kinds of problems we study. For linear ODEs, the solutions that can be obtained by Borel summation are indexed by singular points on the Borel plane. Similarly, integrals over Lefschetz thimbles can be recast as Laplace integrals along rays departing from singular points. ========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_mathematique PRENOM NOM »(indiquez vos propres prénom et nom) et laissez le corps du message vide.

ANNULÉ ET REPORTÉIn this talk we will revisit the bootstrap hypothesis in the two-dimensional case from a mathematical perspective. The bootstrap equations is a consistency for the CFT four-point correlation functions. Therefore, the following question is not mathematically clear: (Math Question) If the four-point correlation functions satisfy the bootstrap equations, can we define a multi-point correlation functions? (Is it convergent and consistent?) After introducing the notion of a full vertex algebra, which is equivalent to the fact that the four-point correlation functions satisfy the bootstrap equations, we will explain that all n-point correlation functions converge and are consistent when the full vertex algebra satisfies certain finiteness. An crucial step in the proof is to show that the operad of configuration spaces acts on representations of the full vertex algebra (under the finiteness assumption). We will explain this idea in detail. 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.