Channel Title: Centre International de Rencontres Mathématiques Channel Description: What is CIRM? http://www.cirm-math.com/our-centre.html <video> Vincent Humilière: Recent progress on groups of area-preserving homeomorphisms Description: Unlike other similar groups, these groups remained very poorly understood for a long time. I'll review some recent progress in two directions: (non)-simplicity and the existence of quasimorphisms. I'll also give some ideas on the proofs which are based on tools from symplectic topology. This is based on joint works with Dan Cristofaro-Gardiner, Cheuk-Yu Mak, Sobhan Seyfaddini, and Ivan Smith. CONFERENCE Recording during the thematic meeting : «Foliations and Diffeomorphism Groups » the December 10, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Johannes Schmidt-Hieber: Statistical Learning in biological neural network Description: Compared to artificial neural networks (ANNs), the brain seems to learn faster, generalize better to new situations and consumes much less energy. ANNs are motivated by the functioning of the brain but differ in several crucial aspects. While ANNs are deterministic, biological neural networks (BNNs) are stochastic. Moreover, it is biologically implausible that the learning of the brain is based on gradient descent. In the past years, statistical theory for artificial neural networks has been developed. The idea now is to extend this to biological neural networks, as the future of AI is likely to draw even more inspiration from biology. In this lecture series we will survey the challenges and present some first statistical risk bounds for different biologically inspired learning rules. CONFERENCE Recording during the thematic meeting : «Meeting in Mathematical Statistics New challenges in high-dimensional statistics» the December 16, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Hélène Eynard-Bontemps: Distortion elements in groups of interval diffeomorphisms Description: An element g of an abstract group G is a distortion element if there exists a finite family S in G such that g belongs to the subgroup generated by S and the wordlength of gn (w.r.t. S) grows sublinearly in n. In this talk, we will be interested in the distortion elements of the group of Cr orientation-preserving diffeomorphisms of the closed interval, for different values of r. In particular, we will present some natural obstructions to distortion (such that the presence of hyperbolic fixed points in C1 regularity and the positivity of the so-called asymptotic distortion in C2 regularity (and higher)), and we will wonder whether they are the only ones. CONFERENCE Recording during the thematic meeting : «Foliations and Diffeomorphism Groups » the December 10, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Kathryn Mann: Groups of Anosov-like homeomorphisms and foliations of the plane - Lecture 1 Description: A theorem of Barbot (building on work of Ghys, Haefliger and others) says that Anosov flows on 3-manifolds are classified up to orbit equivalence by the data of a pair of transverse foliations of the plane and an action of the fundamental group of the 3-manifold. In recent work with T. Barthelmé, as well as C. Bonatti, S. Fenley and S. Frankel, we have been developing an abstract theory of Anosov-like group actions of bifoliated planes, applicable both to the study of flows and as an interesting class of foliation-preserving dynamical systems in its own right. This minicourse will explain some of this theory and the connections between flows and group actions in dimensions 1, 2 and 3. CONFERENCE Recording during the thematic meeting : «Foliations and Diffeomorphism Groups » the December 09, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> New call for proposals to organize an event at CIRM Description: </video> <video> Claire Boyer: Attention layers provably solve single-location regression Description: Attention-based models, such as Transformer, excel across various tasks but lack a comprehensive theoretical understanding, especially regarding token-wise sparsity and internal linear representations. To address this gap, we introduce the single-location regression task, where only one token in a sequence determines the output, and its position is a latent random variable, retrievable via a linear projection of the input. To solve this task, we propose a dedicated predictor, which turns out to be a simplified version of a non-linear self-attention layer. We study its theoretical properties, by showing its asymptotic Bayes optimality and analyzing its training dynamics. In particular, despite the non-convex nature of the problem, the predictor effectively learns the underlying structure. This work highlights the capacity of attention mechanisms to handle sparse token information and internal linear structures. CONFERENCE Recording during the thematic meeting : «Meeting in Mathematical Statistics New challenges in high-dimensional statistics» the December 19, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Yannick Baraud: From robust tests to robust Bayes-like posterior distribution Description: We address the problem of estimating the distribution of presumed i.i.d. observations within the framework of Bayesian statistics. We propose a new posterior distribution that shares some similarities with the classical Bayesian one. In particular, when the statistical model is exact, we show that this new posterior distribution concentrates its mass around the target distribution, just as the classical Bayes posterior would do. However, unlike the Bayes posterior, we prove that these concentration properties remain stable when the equidistribution assumption is violated or when the data are i.i.d. with a distribution that does not belong to our model but only lies close enough to it. The results we obtain are non-asymptotic and involve explicit numerical constants. CONFERENCE Recording during the thematic meeting : «Meeting in Mathematical Statistics New challenges in high-dimensional statistics» the December 16, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Chao Gao: Are adaptive robust confidence intervals possible? Description: We study the construction of confidence intervals under Huber's contamination model. When the contamination proportion is unknown, we characterize the necessary adaptation cost of the problem. In particular, for Gaussian location model, the optimal length of an adaptive confidence interval is proved to be exponentially wider than that of a non-adaptive one. Results for general location models will be discussed. In addition, we also consider the same problem in a network setting for an Erdos-Renyi graph with node contamination. It will be shown that the hardness of the adaptive confidence interval construction is implied by the detection threshold between Erdos-Renyi model and stochastic block model. CONFERENCE Recording during the thematic meeting : «Meeting in Mathematical Statistics New challenges in high-dimensional statistics» the December 16, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Interview at CIRM: Yilin Wang Description: Yilin Wang, mathématicienne Professeure junior en mathématiques à l'IHES depuis 2022 Yilin Wang travaille sur des sujets à l’interface de l’analyse complexe et de la théorie des probabilités. Ses recherches portent sur des thèmes qui visent à éclairer les connexions entre la géométrie conforme aléatoire, la théorie des fonctions géométriques et la théorie de Teichmüller. Née en Chine en 1991, Yilin Wang rejoint la France pour ses études supérieures et obtient un Master scientifique en Probabilités et Statistiques à l’Université Paris-Saclay. Diplômée en 2019 d’un doctorat de l’École polytechnique fédérale (ETH) de Zurich, sous la supervision de Wendelin Werner (médaille Fields 2006), Yilin Wang rejoint le Massachusetts Institute of Technology (MIT) en tant que C.L.E. Moore Instructor, puis le Mathematical Sciences Research Institute de Berkeley (MSRI) en Californie en tant que Strauch Postdoctoral fellow. Le 10 juin 2022, elle rejoint l’IHES en tant que professeure junior, devenant ainsi la première titulaire d’un prestigieux poste de professeur junior à l’IHES, financé grâce au soutien de la Fondation Simons. Depuis 2023, Yilin Wang est le Principal Investigator du programme ERC – Starting Grant « Connecting Random Conformal Geometry and Teichmüller Theory » (RaConTeich), financé par le programme de recherche et d’innovation Horizon Europe de l’Union européenne, dans le cadre de la convention de subvention n°101116694. Prix New Frontiers Maryam Mirzakhani (2022) ERC Stating Grant (2023) Prix Salem (2024) https://en.wikipedia.org/wiki/Salem_Prize (Texte IHES) - https://www.ihes.fr/en/professeur/yilin-wang-2/ Interview/Realization/Post-production: Stéphanie Vareilles 16/07/2024, Sevilla, Spain ------ Yilin Wang, mathematician Junior Professor of Mathematics at IHES since 2022 Yilin Wang works on topics at the interface of complex analysis and probability theory. Her research focuses on topics that aim to illuminate the connections between random conformal geometry, geometric function theory and Teichmüller theory. Born in China in 1991, Yilin Wang moved to France for her graduate studies and obtained a Master of Science in Probability and Statistics at the Université Paris-Saclay. Graduating in 2019 with a PhD from the Swiss Federal Institute of Technology (ETH) Zurich, under the supervision of Wendelin Werner (Fields Medal 2006), Yilin Wang joins the Massachusetts Institute of Technology (MIT) as a C.L.E. Moore Instructor, then the Mathematical Sciences Research Institute Berkeley (MSRI) in California as a Strauch Postdoctoral fellow. On June 10, 2022, she joined IHES as a Junior Professor, becoming the first holder of a prestigious Junior Professorship at IHES, funded with support from the Simons Foundation. Since 2023, Yilin Wang has been Principal Investigator of the ERC - Starting Grant program “Connecting Random Conformal Geometry and Teichmüller Theory” (RaConTeich), funded by the European Union's Horizon Europe research and innovation program, under grant agreement no. 101116694. (Bio from IHES) - https://www.ihes.fr/professeur/yilin-wang/ Interview/Realization/Post-production: Stéphanie Vareilles 16/07/2024, Sevilla, Spain Videos: https://www.carmin.tv/en/speakers/yilin-wang https://en.wikipedia.org/wiki/Salem_Prize ----- Géométrie conforme aléatoire : Yilin Wang est lauréate de l'ERC Starting Grant 2023 (CNRS Mathématiques https://www.insmi.cnrs.fr/fr/cnrsinfo/geometrie-conforme-aleatoire-yilin-wang-est-laureate-de-lerc-starting-grant-2023- https://www.insmi.cnrs.fr/fr/personne/yilin-wang) </video> <video> Christian Bonatti: Foliations on the plane R2,pre-laminations on the circle S1, group actions on... Description: Any (at most countable) family of pairwise transverse (even singular, with saddle or prong singularities) foliations on the plane R² admits a compactification (as the disc D²) by a circle at infinity so that every ray in a leaf tends to a point on the circle, and this compactification is unique up to two natural requirements. Thus every leaf corresponds to a pair of points on the circle. With Th. Barthelmé and K. Mann, we consider the reverse problem and we give a complete answer to the two following questions: Q1: (realization) Under which hypotheses two sets L⁺, L⁻ of pairs of points on the circle are precisely the pairs of endpoints of leaves of two transverse foliations (we give the answer for singular, and also for nonsingular foliations, and we prove that the foliations are uniquely determined). More important is the second question: Q2: (completion) Under which hypotheses two sets l⁺,l⁻ or pair of points on the circle correspond the pairs of endpoints of a dense subset of leaves of two transverse foliations (singular or nonsingular, and uniqueness). The uniqueness implies that any group action on the circle preserving l⁺,l⁻ extends in an action on the disc preserving the corresponding foliations. This allows us to prove that if an action G - Homeo_+(S¹) of a group on the circle is induced by an Anosov-like action G - Homeo_+(D²), then this action is unique and completely determined by the action on the circle. With Th. Marty, we consider the case of 1 (singular or not) foliation and we give a complete answer to the following questions Q3: (realization) Under which hypotheses a set L of pairs of points on the circle is precisely the set of pairs of endpoints of leaves of a foliation, Q4: (completion) Under which hypotheses a set l of pairs of points on the circle corresponds to the pairs of endpoints of a dense subset of leaves of a foliation and we prove again the uniqueness. CONFERENCE Recording during the thematic meeting : «Foliations and Diffeomorphism Groups » the December 13, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Rina Foygel Barber: An introduction to conformal prediction and distribution-free inference Description: This two-part tutorial will introduce the framework of conformal prediction, and will provide an overview of both theoretical foundations and practical methodologies in this field. In the first part of the tutorial, we will cover methods including holdout set methods, full conformal prediction, cross-validation based methods, calibration procedures, and more, with emphasis on how these methods can be adapted to a range of settings to achieve robust uncertainty quantification without compromising on accuracy. In the second part, we will cover some recent extensions that allow the methodology to be applied in broader settings, such as weighted conformal prediction, localized methods, online conformal prediction, and outlier detection. CONFERENCE Recording during the thematic meeting : «Meeting in Mathematical Statistics New challenges in high-dimensional statistics» the December 19, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Emmanuel Militon: Dynamics of surface homeomorphisms and fine curve graph Description: The fine curve graph of a closed surface is a graph on which the group of homeomorphisms of the surface acts faithfully by isometries. This graph is Gromov-hyperbolic. In this talk, we will explore the links between the dynamics of a surface homeomorphism and the type of isometry of its action on the fine curve graph. Joint works with Jonathan Bowden, Sebastian Hensel, Kathryn Mann, and Richard Webb and with Pierre-Antoine Guihéneuf. CONFERENCE Recording during the thematic meeting : «Foliations and Diffeomorphism Groups » the December 12, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Thomas Massoni: Taut foliations through a contact lens Description: Recent work with Nariman and with Fournier-Facio-Nariman determines the bounded cohomology of some familiar diffeomorphism groups. The results differ from what is known or expected in ordinary cohomology. Another way to phrase this is that certain classical characteristic classes are unbounded. The goal of this lecture is to show how some ideas from ergodic theory are useful to prove such cohomological results. CONFERENCE Recording during the thematic meeting : «Foliations and Diffeomorphism Groups » the December 09, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Sang-Hyun Kim : Critical regularity and subexponential growth Description: Two groups are elementarily equivalent if they have the same sets of true firstorder group theoretic sentences. We prove that if the homeomorphism groups of two compact connected manifolds are elementarily equivalent, then the manifolds are homeomorphic. This generalizes Whittaker's theorem on isomorphic homeomorphism groups (1963) without relying on it. Joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS). CONFERENCE Recording during the thematic meeting : «Foliations and Diffeomorphism Groups » the December 12, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video> <video> Frédéric le Roux: Torus homeomorphisms and the fine curve graph Description: In this joint work with Sebastian Hensel, we continue the work of Bowden Hensel-Mann-Militon-Webb relating the rotation set of a torus homeomorphism to the action on the fine curve graph. We show in particular that the shape of a ""big"" rotation set is determined by the fixed points on the Gromov boundary of the graph. CONFERENCE Recording during the thematic meeting : «Foliations and Diffeomorphism Groups » the December 13, 2024 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker : Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, bibliographies, Mathematics Subject Classification - Multi-criteria search by author, title, tags, mathematical area </video>

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