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DTSTART:20190331T010000
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DTSTART:20191027T010000
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DTSTART:20200329T010000
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DTSTART:20201025T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200225T160000
DTEND;TZID=Europe/Paris:20200225T173000
DTSTAMP:20260419T074405
CREATED:20200225T150000Z
LAST-MODIFIED:20211025T103813Z
UID:8543-1582646400-1582651800@www.math.ens.psl.eu
SUMMARY:Autour d'un théorème d'approximation d'Artin
DESCRIPTION:(avec Tom Scanlon)J’exposerai un résultat d’élimination des quantificateurs pour les corps henséliens de degré d’imperfection fini\, relativement à la famille uniforme de tous les groupes RV_gamma = K^\,imes/1+gamma m. Ce résultat permet alors de démontrer que toute extension dense séparable de corps henséliens de même degré d’imperfection fini est élémentaire. En particulier\, l’extension F_p(t)^h leq  F_p((t)) est élémentaire. Ce dernier énoncé précise un résultat d’Artin selon lequel elle est existentiellement close.
URL:https://www.math.ens.psl.eu/evenement/autour-dun-theoreme-dapproximation-dartin/
LOCATION:Salle 2015 Sophie Germain
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200218T150000
DTEND;TZID=Europe/Paris:20200218T170000
DTSTAMP:20260419T074405
CREATED:20200218T140000Z
LAST-MODIFIED:20211104T134933Z
UID:8542-1582038000-1582045200@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00-14.45 David Hume (Oxford)\, Three dichotomies for connected unimodular Lie groups15.00-15.45 Nikolay Bogachev (Skoltech & MIPT)\, Arithmetic hyperbolic reflection groups16.15-17.00 Daniel Woodhouse (Oxford)\, Action rigidity of free products of hyperbolic manifold groups
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-9/
LOCATION:Salle W (DMA ENS)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200131T160000
DTEND;TZID=Europe/Paris:20200131T172000
DTSTAMP:20260419T074405
CREATED:20200131T150000Z
LAST-MODIFIED:20211025T103757Z
UID:8538-1580486400-1580491200@www.math.ens.psl.eu
SUMMARY:Geometric quadratic Chabauty.
DESCRIPTION:Determining all rational points on a curve of genus at least 2 can be difficult. Chabauty’s method (1941) is to intersect\, for a prime number p\, in the p-adic Lie group of p-adic points of the jacobian\, the closure of the Mordell-Weil group with the p-adic points of the curve. If the Mordell-Weil rank is less than the genus then this method has never failed. Minhyong Kim’s non-abelian Chabauty programme aims to remove the condition on the rank. The simplest case\, called quadratic Chabauty\, was developed by Balakrishnan\, Dogra\, Mueller\, Tuitman and Vonk\, and applied in a tour de force to the so-called cursed curve (rank and genus both 3). This article aims to make the quadratic Chabauty method small and geometric again\, by describing it in terms of only `simple algebraic geometry’ (line bundles over the jacobian and models over the integers).
URL:https://www.math.ens.psl.eu/evenement/geometric-quadratic-chabauty/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200131T141500
DTEND;TZID=Europe/Paris:20200131T153500
DTSTAMP:20260419T074405
CREATED:20200131T131500Z
LAST-MODIFIED:20211104T141458Z
UID:8541-1580480100-1580484900@www.math.ens.psl.eu
SUMMARY:Quantitative Fundamental Theorem of Algebra
DESCRIPTION:Using subresultants\, we modify a recent real-algebraic proof due to Eisermann of the Fundamental Theorem of Algebra ([FTA]) to obtain the following quantitative information: in order to prove the [FTA] for polynomials of degree d\, the Intermediate Value Theorem ([IVT]) is requested to hold for real polynomials of degree at most d^2. We also explain that the classical algebraic proof due to Laplace requires [IVT] for real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs.
URL:https://www.math.ens.psl.eu/evenement/quantitative-fundamental-theorem-of-algebra/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200131T110000
DTEND;TZID=Europe/Paris:20200131T122000
DTSTAMP:20260419T074405
CREATED:20200131T100000Z
LAST-MODIFIED:20211025T103807Z
UID:8540-1580468400-1580473200@www.math.ens.psl.eu
SUMMARY:Classification des imaginaires dans VFA
DESCRIPTION:(travail en commun avec Silvain Rideau-Kikuchi)Les imaginaires (c’est-à-dire les quotients définissables) dans la théorie ACVF des corpsalgébriquement clos non-trivialement valués sont classifiés par les sortes “géométriques”.Ceci est un résultat fondamental dû à Haskell\, Hrushovski et Macpherson. En utilisantl’approche via la densité des types définissables/invariants\, nous donnons une réductiondes imaginaires dans des corps valués henséliens\, sous des hypothèses assez générales\,aux sortes géométriques et à des imaginaires de RV avec des sortes pour certains espacesvectoriels de dimension finie sur le corps résiduel.
URL:https://www.math.ens.psl.eu/evenement/classification-des-imaginaires-dans-vfa/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200121T150000
DTEND;TZID=Europe/Paris:20200121T170000
DTSTAMP:20260419T074405
CREATED:20200121T140000Z
LAST-MODIFIED:20211104T135010Z
UID:8539-1579618800-1579626000@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00-14.45 Francois Dahmani (Grenoble)\, Relative hyperbolicity of free-by-cyclic groups\, and conjugacy between automorphisms of free groups15.00-15.45 Tatiana Smirnova-Nagnibeda (Geneva)\, Various types of spectra and spectral measures on Schreier and Cayley graphs16.15-17.00 Urs Lang (ETH Zurich)\, Characterizations and asymptotic geometry of rank-n-hyperbolic spaces
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-8/
LOCATION:Salle W (DMA ENS)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200107T160000
DTEND;TZID=Europe/Paris:20200107T173000
DTSTAMP:20260419T074405
CREATED:20200107T150000Z
LAST-MODIFIED:20211104T122755Z
UID:8536-1578412800-1578418200@www.math.ens.psl.eu
SUMMARY:Groupes de Lie et définissabilité le cas (non) linéaire.
DESCRIPTION:Entre les catégories des groupes semialgébriques et des groupes de Lie se trouve la catégorie des groupes définissables dans une expansion o-minimale des réels (noté simplement définissables dans la suite). Puisque tout groupe définissable peut être équipé d’une structure de groupe de Lie (Pillay 1989)\, il est intéressant de savoir sous quelles conditions un groupe de Lie est isomorphe (au sens de Lie) à un groupe définissable. Starchenko\, Onshuus et Conversano ont répondu à cette question dans le cas où le groupe est résoluble (2016). Nous nous intéresserons ici au cas linéaire puis si le temps le permet au cas général.
URL:https://www.math.ens.psl.eu/evenement/groupes-de-lie-et-definissabilite-le-cas-non-lineaire/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191217T150000
DTEND;TZID=Europe/Paris:20191217T170000
DTSTAMP:20260419T074405
CREATED:20191217T140000Z
LAST-MODIFIED:20211104T135037Z
UID:8535-1576594800-1576602000@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:15.00-15.45 Ashot Minasyan (Southampton)\, CAT(0) groups with exotic properties16.15-17.00 Assaf Naor (Princeton)\, Vertical-versus-horizontal isoperimetry*NOTE* Urs Lang’s talk has been moved to January 21
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-7/
LOCATION:Salle W (DMA ENS)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191112T140000
DTEND;TZID=Europe/Paris:20191112T170000
DTSTAMP:20260419T074405
CREATED:20191112T130000Z
LAST-MODIFIED:20211104T133906Z
UID:8533-1573567200-1573578000@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00-14.45 Peter Haissinsky (Université d’Aix-Marseille)\, Quasi-isometric rigidity of 3-manifold groups.15.00-15.45 Nima Hoda (ENS Paris)\, Shortcut graphs and groups.16.15-17.00 Elia Fioravanti (Oxford)\, Cross ratios on cube complexesand marked length-spectrum rigidity.
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-6/
LOCATION:Salle W (DMA ENS)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191110T110000
DTEND;TZID=Europe/Paris:20191110T123000
DTSTAMP:20260419T074405
CREATED:20191110T100000Z
LAST-MODIFIED:20211104T112900Z
UID:14071-1573383600-1573389000@www.math.ens.psl.eu
SUMMARY:A valuative approach to the inner geometry of surfaces
DESCRIPTION:Lipschitz geometry is a branch of singularity theory that studies the metric data of a germ of a complex analytic space.I will discuss a new approach to the study of such metric germs\, and in particular of an invariant called Lipschitz inner rate\, based on the combinatorics of a space of valuations\, the so-called non-archimedean link of the singularity. I will describe completely the inner metric structure of a complex surface germ showing that its inner rates both determine and are determined by global geometric data: the topology of the germ\, its hyperplane sections\, and its generic polar curves.This is a joint work with André Belotto and Anne Pichon.
URL:https://www.math.ens.psl.eu/evenement/a-valuative-approach-to-the-inner-geometry-of-surfaces-2/
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191108T160000
DTEND;TZID=Europe/Paris:20191108T172000
DTSTAMP:20260419T074405
CREATED:20191108T150000Z
LAST-MODIFIED:20211104T125730Z
UID:8532-1573228800-1573233600@www.math.ens.psl.eu
SUMMARY:Une construction d'extensions faiblement non ramifiées d'un anneau de valuation
DESCRIPTION:Étant donné un anneau de valuation V de corps résiduel F et contenant un corps k\, et une extension k’ de k\, on cherche à construire une extension V’ de V contenant k’\, d’idéal maximal engendré par celui de V\, et de corps résiduel composé de F et k’. On y parvient notamment si F ou k’ est séparable sur k.
URL:https://www.math.ens.psl.eu/evenement/une-construction-dextensions-faiblement-non-ramifiees-dun-anneau-de-valuation/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191108T141500
DTEND;TZID=Europe/Paris:20191108T153500
DTSTAMP:20260419T074405
CREATED:20191108T131500Z
LAST-MODIFIED:20211104T125154Z
UID:8530-1573222500-1573227300@www.math.ens.psl.eu
SUMMARY:The Mumford-Tate conjecture implies the algebraic Sato-Tate conjecture
DESCRIPTION:The famous Mumford-Tate conjecture asserts that\, for every prime number l\, Hodge cycles are Q_l linear combinations of Tate cycles\, through Artin’s comparisons theorems between Betti and étale cohomology. The algebraic Sato-Tate conjecture\, introduced by Serre and developed by Banaszak and Kedlaya\, is a powerful tool in order to prove new instances of the generalized Sato-Tate conjecture. This previous conjecture is related with the equidistribution of Frobenius traces.Our main goal is to prove that the Mumford-Tate conjecture for an abelian variety A implies the algebraic Sato-Tate conjecture for A. The relevance of this result lies mainly in the fact that the list of known cases of the Mumford-Tate conjecture was up to now a lot longer than the list of known cases of the algebraic Sato-Tate conjecture. This is a joint work with Johan Commelin.
URL:https://www.math.ens.psl.eu/evenement/the-mumford-tate-conjecture-implies-the-algebraic-sato-tate-conjecture/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191108T110000
DTEND;TZID=Europe/Paris:20191108T122000
DTSTAMP:20260419T074405
CREATED:20191108T100000Z
LAST-MODIFIED:20211104T130247Z
UID:8531-1573210800-1573215600@www.math.ens.psl.eu
SUMMARY:Characterizing NIP henselian fields
DESCRIPTION:In this talk\, we characterize NIP henselian valued fields modulo the theory of their residue field. Assuming the conjecture that every infinite NIP field is either separably closed\, real closed or admits a non-trivial henselian valuation\, this allows us to obtain a characterization of all theories of NIP fields.
URL:https://www.math.ens.psl.eu/evenement/characterizing-nip-henselian-fields/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191105T160000
DTEND;TZID=Europe/Paris:20191105T173000
DTSTAMP:20260419T074405
CREATED:20191105T150000Z
LAST-MODIFIED:20211104T131047Z
UID:8527-1572969600-1572975000@www.math.ens.psl.eu
SUMMARY:Expansions de l'arithmétique de Presburger avec la propriété d'échange
DESCRIPTION:Soit G un groupe élémentairement équivalent à Z dans le langage de Presburger L_Pres. Soit L une expansion du langage L_Pres. On dit que la théorie de (G\, L) est L_Pres-minimale si tout sous-ensemble L-définissable de M est L_Pres-définissable (où M est un modèle de la théorie). Si G=Z\, des résultats de C. Michaux et R. Villemaire impliquent que Th(Z\, L) est L_Pres-minimale ssi la clôture algébrique a la propriété d’échange. Dans cet exposé\, je discuterai le cadre général. En particulier\, nous verrons que Th(G\,L) est L_Pres-minimale ssi la clôture algébrique a la propriété d’échange et tout sous-ensemble définissable borné de G a un maximum.
URL:https://www.math.ens.psl.eu/evenement/expansions-de-larithmetique-de-presburger-avec-la-propriete-dechange/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191029T160000
DTEND;TZID=Europe/Paris:20191029T173000
DTSTAMP:20260419T074405
CREATED:20191029T150000Z
LAST-MODIFIED:20211104T140810Z
UID:8529-1572364800-1572370200@www.math.ens.psl.eu
SUMMARY:Model theory of proalgebraic groups
DESCRIPTION:Inspired by the model theoretic study of profinite groups\, we discuss the foundations of a model theoretic approach to proalgebraic groups. Our axiomatization is based on the tannakian philosophy. Through a tensor analog of skeletal categories we are able to consider neutral tannakian categories with a fibre functor as many-sorted first order structures. The theory of a diagonalizable proalgebraic group is well understood. It is determined by the theory of the base field and the theory of its character group. This is joint work with Anand Pillay.
URL:https://www.math.ens.psl.eu/evenement/model-theory-of-proalgebraic-groups/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191029T140000
DTEND;TZID=Europe/Paris:20191029T170000
DTSTAMP:20260419T074405
CREATED:20191029T130000Z
LAST-MODIFIED:20211104T135125Z
UID:8528-1572357600-1572368400@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00-14.45 Christophe Pittet (Genève)\, The exact convergence rate in the ergodic theorem of Lubotzky Phillips Sarnak.15.00-15.45 Thiebout Delabie (Orsay)\, High dimensional cuts and coarse embedding.16.15-17.00 Alina Vdovina (Newcastle)\, Ramanujan cubical complexes as higher-dimensional expanders.
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-5/
LOCATION:Salle W (DMA ENS)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191022T160000
DTEND;TZID=Europe/Paris:20191022T173000
DTSTAMP:20260419T074405
CREATED:20191022T140000Z
LAST-MODIFIED:20211025T103725Z
UID:8526-1571760000-1571765400@www.math.ens.psl.eu
SUMMARY:The transitivity of Kim-independence
DESCRIPTION:The class of NSOP_1 theories contains the simple theories and many interesting non-simple theories\, such as the omega-free PAC fields or generic vector spaces with a non-degenerate bilinear form. With Itay Kaplan\, we introduced Kim-independence which agrees with non-forking independence within the simple theories and shares many of its nice properties within the simple NSOP_1 context. One very basic roadblock in lifting simplicity theory to the NSOP_1 setting\, however\, was transitivity: a free extension of a free extension should still be a free extension. This is almost immediate for non-forking extensions in a simple theory\, but becomes more involved for free extensions in the sense of Kim-independence. We will describe and motivate the basic theory\, and then discuss our recent proof of transitivity. This is joint with Itay Kaplan.
URL:https://www.math.ens.psl.eu/evenement/the-transitivity-of-kim-independence/
LOCATION:Sophie Germain salle 1016
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191011T160000
DTEND;TZID=Europe/Paris:20191011T173000
DTSTAMP:20260419T074405
CREATED:20191011T140000Z
LAST-MODIFIED:20211025T103721Z
UID:8524-1570809600-1570815000@www.math.ens.psl.eu
SUMMARY:H-minimality
DESCRIPTION:My goal\, in this talk\, is to explain a new notion of minimality for (characteristic zero) Henselian fields\, which generalizes C-minimality\, P-minimality and V-minimality and puts no restriction on the residue field or valued group contrary to these previous notions. This new notion\, h-minimality\, can be defined\, analogously to other minimality notions\, by asking that 1-types\, over algebraically closed sets\, are entirely determined by their reduct to some sublanguage – in that case the pure language of valued fields. However\, contrary to what happens with other minimality notions\, particular care has to be taken with regards to the parameters. In fact\, we define a family of notions: l-h-min for l a natural number or omega. My second goal in this talk will be to explain the various geometric properties that follow form h-minimality\, among which the well-known Jacobian property\, but also higher degree and higher dimensional versions of that property.
URL:https://www.math.ens.psl.eu/evenement/h-minimality/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191011T141500
DTEND;TZID=Europe/Paris:20191011T154500
DTSTAMP:20260419T074405
CREATED:20191011T121500Z
LAST-MODIFIED:20211025T103723Z
UID:8525-1570803300-1570808700@www.math.ens.psl.eu
SUMMARY:Quantifier elimination in algebraically closed valued fields in the analytic language: a geometric approach
DESCRIPTION:I will present a work on flattening by blow-ups in the context of Berkovich geometry (inspired by Raynaud and Gruson’s paper on the same topic in the scheme-theoretic setting)\, and explain how it gives rise to the description of the image of an arbitrary analytic map between two compact Berkovich spaces\, and why this description is (very likely) related to quantifier elimination in the Lipshitz-Cluckers variant of Lipshitz-Robinson’s analytic language. (I plan to spend most of the talk discussing the results rather than their proofs.)
URL:https://www.math.ens.psl.eu/evenement/quantifier-elimination-in-algebraically-closed-valued-fields-in-the-analytic-language-a-geometric-approach/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191008T160000
DTEND;TZID=Europe/Paris:20191008T173000
DTSTAMP:20260419T074405
CREATED:20191008T140000Z
LAST-MODIFIED:20211104T140837Z
UID:8522-1570550400-1570555800@www.math.ens.psl.eu
SUMMARY:An abstract elementary class framework for fields with commuting automorphisms
DESCRIPTION:We take a look at structures that consist of a field together with finitely many distinguished field automorphisms required to commute. The theory of fields with one distinguished automorphism has a model companion known as ACFA\, which Z. Chatzidakis and E. Hrushovski have studied in depth. However\, Hrushovski has proved that if you look at fields with two or more commuting automorphisms\, then the existentially closed models of the theory do not form a first order model class. This leads us to investigate them within a non-elementary framework. One way of doing non-elementary model theory is to move from elementary classes to the more general setting of abstract elementary classes (AECs). In the first order world\, classes of structures are usually defined syntactically as model classes of a given first order theory. An AEC is defined more semantically\, as a class of structures together with a binary relation that generalises the first-order elementary submodel relation. In this talk\, we go through some basics of AECs and present an AEC framework for studying fields with commuting automorphisms.
URL:https://www.math.ens.psl.eu/evenement/an-abstract-elementary-class-framework-for-fields-with-commuting-automorphisms/
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191005T141500
DTEND;TZID=Europe/Paris:20191005T154500
DTSTAMP:20260419T074405
CREATED:20191005T121500Z
LAST-MODIFIED:20211104T112259Z
UID:14057-1570284900-1570290300@www.math.ens.psl.eu
SUMMARY:Point-wise surjective presentations of stacks\, or why I am not afraid of (infinity) stacks anymore
DESCRIPTION:Any algebraic stack X can be represented by a groupoid object in the category of schemes: that is\, a pair of schemes Ob\, Mor and morphisms source\, target: Mor &rarr
URL:https://www.math.ens.psl.eu/evenement/point-wise-surjective-presentations-of-stacks-or-why-i-am-not-afraid-of-infinity-stacks-anymore-2/
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191001T160000
DTEND;TZID=Europe/Paris:20191001T173000
DTSTAMP:20260419T074405
CREATED:20191001T140000Z
LAST-MODIFIED:20211025T103654Z
UID:8515-1569945600-1569951000@www.math.ens.psl.eu
SUMMARY:Sous-groupes qui pavent génériquement et géométrie des involutions
DESCRIPTION:(En collaboration avec Joshua Wiscons)L’exposé mélange théorie des modèles\, théorie des groupes\, et algèbre géométrique. On y parlera de groupes de rang de Morley fini\, mais il suffit de savoir naïvement ce qu’est une dimension à valeurs entières\, sans devoir maîtriser les finesses de la conjecture de Cherlin-Zilber.Un groupe abstrait porte peu d’information de nature géométrique\, même au sens des géométries d’incidence\, et c’est toujours remarquable si cela se produit.Le pur groupe SO(3\,R)\, par exemple\, permet de redéfinir l’espace projectif réel. PGL(2\,C) permet presque la même chose : il définit un fragment générique de l’espace projectif complexe. En fait cette situation est naturellement liée à la distribution des involutions et aux intersections entre conjugués de leur centralisateur\, qui pavent génériquement le groupe ambiant (tout cela sera expliqué dans SO(3\,R) et PGL(2\,C)).En suivant cette piste on peut obtenir des énoncés étonnamment forts\, généralisant au passage divers classiques sur les mauvais groupes ou sur les groupes définissablement linéaires de rang de Morley fini. On conjecture également que cette géométrie des involutions annonce un nouveau théorème d’identification pour PGL(2\, K).
URL:https://www.math.ens.psl.eu/evenement/sous-groupes-qui-pavent-generiquement-et-geometrie-des-involutions/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190924T160000
DTEND;TZID=Europe/Paris:20190924T173000
DTSTAMP:20260419T074405
CREATED:20190924T140000Z
LAST-MODIFIED:20211104T140910Z
UID:8514-1569340800-1569346200@www.math.ens.psl.eu
SUMMARY:H-structures
DESCRIPTION:A complete theory T is called geometric if the algebraic closure has the exchange property in all models of T and the theory eliminates the quantifier exists infinity. In such theories there is a rudimentary notion of independence given by algebraic independence. Examples of geometric theories include SU-rank one theories and dense o-minimal theories.An expansion of a model M of T by a unary predicate H is called dense-codense if for every finite dimensional subset A of M and every non algebraic type p(x) over A\, there is a realization of p(x) in H(M) and another one which is not algebraic over AH(M). A dense-codense expansion is called an H-structure if in addition H(M) is algebraically independent.In this talk we will talk about the basic properties of H-structures and how the new structure can be understood as a tame expansion of the original structure M. We will discuss groups definable in this expansion. We will also present some recent results on the special case when M is the ultrapower of a one-dimensional asymptotic class.This talk includes joint work with E. Vassiliev and D. Garcia and T. Zou.
URL:https://www.math.ens.psl.eu/evenement/h-structures/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190810T160000
DTEND;TZID=Europe/Paris:20190810T173000
DTSTAMP:20260419T074405
CREATED:20190810T140000Z
LAST-MODIFIED:20211104T112705Z
UID:14070-1565452800-1565458200@www.math.ens.psl.eu
SUMMARY:An abstract elementary class framework for fields with commuting automorphisms
DESCRIPTION:We take a look at structures that consist of a field together with finitely many distinguished field automorphisms required to commute. The theory of fields with one distinguished automorphism has a model companion known as ACFA\, which Z. Chatzidakis and E. Hrushovski have studied in depth. However\, Hrushovski has proved that if you look at fields with two or more commuting automorphisms\, then the existentially closed models of the theory do not form a first order model class. This leads us to investigate them within a non-elementary framework. One way of doing non-elementary model theory is to move from elementary classes to the more general setting of abstract elementary classes (AECs). In the first order world\, classes of structures are usually defined syntactically as model classes of a given first order theory. An AEC is defined more semantically\, as a class of structures together with a binary relation that generalises the first-order elementary submodel relation. In this talk\, we go through some basics of AECs and present an AEC framework for studying fields with commuting automorphisms.
URL:https://www.math.ens.psl.eu/evenement/an-abstract-elementary-class-framework-for-fields-with-commuting-automorphisms-2/
CATEGORIES:Théorie des Modèles et Groupes
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190618T140000
DTEND;TZID=Europe/Paris:20190618T170000
DTSTAMP:20260419T074405
CREATED:20190618T120000Z
LAST-MODIFIED:20211104T135150Z
UID:8513-1560866400-1560877200@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00-14.45 Katrin Tent (Munster)\, Burnside groups of relatively small odd exponent15.00-15.45 Arindam Biswas (Vienne)\, On minimal complements in groups16.15-16.45 Laurent Bartholdi (Institut d’études avancées\, ENS Lyon)\, Dimension series and homotopy groups of spheres
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-4/
LOCATION:IHP salle 1
CATEGORIES:Séminaire de théorie des groupes à l’ENS
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190514T140000
DTEND;TZID=Europe/Paris:20190514T170000
DTSTAMP:20260419T074405
CREATED:20190514T120000Z
LAST-MODIFIED:20211104T135214Z
UID:8510-1557842400-1557853200@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00-14.45 Stefan Witzel (Ecole Polytehchnique)15.00-15.45 Katie Vokes (IHES)15.45-16.15 coffee break16.15-16.45 Adrien Le Boudec (ENS Lyon)Stefan Witzel\, Arithmetic approximate groups and their finiteness propertiesI will talk about approximate groups\, a geometric generalization of groups. Approximate groups were discovered independently in various contexts and I will describe how they arise very naturally in the context of arithmetic groups. I will then explain how to extend topological finiteness properties of groups to approximate groups. This allows to make a connection betweenarithmetic groups in positive characteristic and arithmetic approximate groups in characteristic zero. The talk is based on joint work with Tobias Hartnick.Katie Vokes\, Hierarchical hyperbolicity of graphs associated to surfacesIn a paper of 2000\, Masur and Minsky studied the geometry of mapping class groups of surfaces using projections to certain Gromov hyperbolic graphs (the curve graphs) associated to subsurfaces. This inspired the definition by Behrstock\, Hagen and Sisto of hierarchically hyperbolic spaces\, which are equipped with similar projection maps\, satisfying conditions which guarantee a structure analogous to that of the mapping class group. I will give some background on these concepts and present a result demonstrating that a large family of graphs associated to surfaces are hierarchically hyperbolic spaces.Adrien Le Boudec\, Simple groups having a wreath product as a geometric modelThe goal of the talk will be to describe groups that are finitelygenerated\, simple\, and that act properly and cocompactly on thenatural Cayley graph of the wreath product A wr F\, where A is afinite group and F a non-abelian free group.
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-3/
LOCATION:Salle W (DMA)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190510T160000
DTEND;TZID=Europe/Paris:20190510T173000
DTSTAMP:20260419T074405
CREATED:20190510T140000Z
LAST-MODIFIED:20211104T132132Z
UID:8507-1557504000-1557509400@www.math.ens.psl.eu
SUMMARY:Non-archimedean and motivic integrals on the Hitchin fibration
DESCRIPTION:Based on mirror symmetry considerations\, Hausel and Thaddeus conjectured an equality between `stringy’ Hodge numbers for moduli spaces of SL_n/PGL_n Higgs bundles. With Michael Groechenig and Paul Ziegler we prove this conjecture using non-archimedean integrals on these moduli spaces\, building on work of Denef-Loeser and Batyrev. Similar ideas also lead to a new proof of the geometric stabilization theorem for anisotropic Hitchin fibers\, a key ingredient in the proof of the fundamental lemma by Ngô.In my talk I will outline the main arguments of the proofs and discuss the adjustments needed\, in order to replace non-archimedean integrals by motivic ones. The latter is joint work with François Loeser.
URL:https://www.math.ens.psl.eu/evenement/non-archimedean-and-motivic-integrals-on-the-hitchin-fibration/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190510T141500
DTEND;TZID=Europe/Paris:20190510T154500
DTSTAMP:20260419T074405
CREATED:20190510T121500Z
LAST-MODIFIED:20211104T141516Z
UID:8509-1557497700-1557503100@www.math.ens.psl.eu
SUMMARY:Point-wise surjective presentations of stacks\, or why I am not afraid of (infinity) stacks anymore
DESCRIPTION:Any algebraic stack X can be represented by a groupoid object in the category of schemes: that is\, a pair of schemes Ob\, Mor and morphisms source\, target: Mor → Ob\, inversion: Mor → Mor\, composition: Mor ×_{Ob} Mor → Mor and identity: Ob → Mor that satisfy certain axioms. Yet this description of the stack X might be misleading.\nNamely\, given a field F which is not algebraically closed\, we have a natural functor between the groupoid (Ob(F)\,Mor(F)) and the groupoid X(F). While this functor is fully faithful\, it is often not essentially surjective.\nIn joint work with Nir Avni (in progress) we show that any algebraic groupoid has a presentation such that this functor will be essentially surjective for many fields (and under some assumptions on the stack\, for any field). The results are also extended to Henselian rings.\nDespite the title\, the talk will be about usual stacks and not infinity-stacks\, yet in some of the proofs it is more convenient to use the language of higher categories and I’ll try to explain why.\nNo prior knowledge of infinity stacks will be assumed\, but a superficial acquaintance with usual stacks will be helpful.
URL:https://www.math.ens.psl.eu/evenement/point-wise-surjective-presentations-of-stacks-or-why-i-am-not-afraid-of-infinity-stacks-anymore/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190510T110000
DTEND;TZID=Europe/Paris:20190510T123000
DTSTAMP:20260419T074405
CREATED:20190510T090000Z
LAST-MODIFIED:20211025T103641Z
UID:8511-1557486000-1557491400@www.math.ens.psl.eu
SUMMARY:Almost strongly minimal ample geometries
DESCRIPTION:The notion of ampleness captures essential properties of projective spaces over fields. It is natural to ask whether any sufficiently ample strongly minimal set arises from an algebraically closed field. In this talk I will explain the question and present recent results on ample strongly minimal structures.
URL:https://www.math.ens.psl.eu/evenement/almost-strongly-minimal-ample-geometries/
CATEGORIES:Séminaire Géométrie et théorie des modèles
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190507T160000
DTEND;TZID=Europe/Paris:20190507T173000
DTSTAMP:20260419T074405
CREATED:20190507T140000Z
LAST-MODIFIED:20211104T140929Z
UID:8508-1557244800-1557250200@www.math.ens.psl.eu
SUMMARY:Groups definable in Presburger arithmetic
DESCRIPTION:I will give a complete description of all groups definable in Presburger arithmetic\, up to finite index subgroups. This builds on previous work on bounded groups in Presburger arithmetic by Mariana Vicaria and Alf Onshuus.
URL:https://www.math.ens.psl.eu/evenement/groups-definable-in-presburger-arithmetic/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
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END:VCALENDAR