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X-WR-CALDESC:évènements pour Département de mathématiques et applications
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TZID:Europe/Paris
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TZNAME:CEST
DTSTART:20190331T010000
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DTSTART:20191027T010000
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DTSTART:20200329T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210115T093000
DTEND;TZID=Europe/Paris:20210115T105000
DTSTAMP:20261026T165845
CREATED:20210115T083000Z
LAST-MODIFIED:20211025T103924Z
UID:8566-1610703000-1610707800@www.math.ens.psl.eu
SUMMARY:An application of surreal numbers to the asymptotic analysis of certain exponential functions
DESCRIPTION:Skolem (1956) studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant 1\, the identity function x\, and such that whenever f and g are in the set\, f+g\, fg and f^g are also in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz (1984) computed the order type of the fragment below 2^(2^x). They did so by studying the possible limits at infinity of the quotient f(x)/g(x) of two functions in the fragment: if g is kept fixed and f varies\, the possible limits form a discrete set of real numbers of order type omega.Using the surreal numbers\, we extend the latter result to the whole class of Skolem functions and we discuss some additional progress towards the conjecture of Skolem. This is joint work with Marcello Mamino (http://arxiv.org/abs/1911.07576\, to appear in the JSL).
URL:https://www.math.ens.psl.eu/evenement/an-application-of-surreal-numbers-to-the-asymptotic-analysis-of-certain-exponential-functions/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201211T090000
DTEND;TZID=Europe/Paris:20201211T102000
DTSTAMP:20261026T165845
CREATED:20201211T080000Z
LAST-MODIFIED:20211104T122913Z
UID:8563-1607677200-1607682000@www.math.ens.psl.eu
SUMMARY:Groups definable in o-minimal structures and algebraic groups
DESCRIPTION:Groups definable in o-minimal structures have been studied by many authors in the last 30 years and include algebraic groups over algebraically closed fields of characteristic 0\, semi-algebraic groups over real closed fields\, important classes of real Lie groups such as abelian groups\, compact groups and linear semisimple groups. In this talk I will present results on groups definable in o-minimal structures\, demonstrating a strong analogy with topological decompositions of linear algebraic groups. Limitations of this analogy will be shown through several examples.
URL:https://www.math.ens.psl.eu/evenement/groups-definable-in-o-minimal-structures-and-algebraic-groups/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201127T090000
DTEND;TZID=Europe/Paris:20201127T100000
DTSTAMP:20261026T165845
CREATED:20201127T080000Z
LAST-MODIFIED:20211104T141134Z
UID:8562-1606467600-1606471200@www.math.ens.psl.eu
SUMMARY:The étale-open topology (suite)
DESCRIPTION:Fix an abstract field K. For each K-variety V\, we will define an “étale-open” topology on the set V(K) of rational points of V. This notion uniformly recovers (1) the Zariski topology on V(K) when K is algebraically closed\, (2) the analytic topology on V(K) when K is the real numbers\, (3) the valuation topology on V(K) when K is almost any henselian field. On pseudo-finite fields\, the étale-open topology seems to be new\, and has some interesting properties.\nThe étale-open topology is mostly of interest when Kis large (also known as ample). On non-large fields\, theétale-open topology is discrete. In fact\, this propertycharacterizes largeness. Using this\, one can recover some well-knownfacts about large fields\, and classify the model-theoretically stablelarge fields. It may be possible to push these arguments towards aclassification of NIP large fields. Joint work with Chieu-Minh Tran\, Erik Walsberg\, and Jinhe Ye.
URL:https://www.math.ens.psl.eu/evenement/the-etale-open-topology-suite/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201113T103000
DTEND;TZID=Europe/Paris:20201113T115000
DTSTAMP:20261026T165845
CREATED:20201113T093000Z
LAST-MODIFIED:20211104T141149Z
UID:8559-1605263400-1605268200@www.math.ens.psl.eu
SUMMARY:Belles paires of valued fields and analytification
DESCRIPTION:In their work\, Hrushovski and Loeser proposed the space V̂ of generically stable types concentrating on V to study the homotopy type of the Berkovich analytification of V. An important feature of V̂ is that it is canonically identified as a projective limit of definable sets in ACVF\, which grants them tools from model theory. In this talk\, we will give a brief introduction to this object and present an alternative approach to internalize various spaces of definable types\, motivated by Poizat’s work on belles paires of stable theories. Several results of interest to model theorists will also be discussed. Particularly\, we recover the space V̂ is strict pro-definable and we propose a model-theoretic counterpart Ṽ of Huber’s analytification. Time permitting\, we will discuss some comparison and lifting results between V̂ and Ṽ. This is a joint project with Pablo Cubides Kovacsics and Martin Hils.
URL:https://www.math.ens.psl.eu/evenement/belles-paires-of-valued-fields-and-analytification/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201113T090000
DTEND;TZID=Europe/Paris:20201113T102000
DTSTAMP:20261026T165845
CREATED:20201113T080000Z
LAST-MODIFIED:20211104T141207Z
UID:8558-1605258000-1605262800@www.math.ens.psl.eu
SUMMARY:The étale-open topology
DESCRIPTION:Fix an abstract field K. For each K-variety V\, we will define an étale-open topology on the set V(K) of rational points of V. This notion uniformly recovers (1) the Zariski topology on V(K) when K is algebraically closed\, (2) the analytic topology on V(K) when K is the real numbers\, (3) the valuation topology on V(K) when K is almost any henselian field. On pseudo-finite fields\, the étale-open topology seems to be new\, and has some interesting properties.The étale-open topology is mostly of interest when K is large (also known as ample). On non-large fields\, the étale-open topology is discrete. In fact\, this property characterizes largeness. Using this\, one can recover some well-known facts about large fields\, and classify the model-theoretically stable large fields. It may be possible to push these arguments towards a classification of NIP large fields. Joint work with Chieu-Minh Tran\, Erik Walsberg\, and Jinhe Ye.
URL:https://www.math.ens.psl.eu/evenement/the-etale-open-topology/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201112T103000
DTEND;TZID=Europe/Paris:20201112T115000
DTSTAMP:20261026T165845
CREATED:20201112T093000Z
LAST-MODIFIED:20211104T121624Z
UID:14111-1605177000-1605181800@www.math.ens.psl.eu
SUMMARY:Cohomology of algebraic varieties over non-archimedean fields
DESCRIPTION:I will report on a joint work with Mário Edmundo and Jinhe Ye in which we introduced a sheaf cohomology theory for algebraic varieties over non-archimedean fields based on Hrushovski-Loeser spaces. After informally framing our main results with respect to classical statements\, I will discuss some details of our construction and the main difficulties arising in this new context. If time allows\, I will further explain how our results allow us to recover results of V. Berkovich on the sheaf cohomology of the analytification of an algebraic variety over a rank 1 complete non-archimedean field.
URL:https://www.math.ens.psl.eu/evenement/cohomology-of-algebraic-varieties-over-non-archimedean-fields-2/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201016T103000
DTEND;TZID=Europe/Paris:20201016T115000
DTSTAMP:20261026T165845
CREATED:20201016T083000Z
LAST-MODIFIED:20211104T141411Z
UID:8557-1602844200-1602849000@www.math.ens.psl.eu
SUMMARY:Tame geometry and diophantine approximation
DESCRIPTION:Tame geometry is the study of structures where the definable sets admit finite complexity. Around 15 years ago Pila and Wilkie discovered a deep connection between tame geometry and diophantine approximation\, in the form of asymptotic estimates on the number of rational points in a tame set (as a function of height). This later led to deep applications in diophantine geometry\, functional transcendence and Hodge theory.I will describe some conjectures and a long-term project around a more effective form of tame geometry\, suited for improving the quality of the diophantine approximation results and their applications. I will try to outline some of the pieces that are already available\, and how they should conjecturally fit together. Finally I will survey some applications of the existing results around the Manin-Mumford conjecture\, the Andre-Oort conjecture\, Galois-orbit lower bounds in Shimura varieties\, unlikely intersections in group schemes\, and some other directions (time permitting).
URL:https://www.math.ens.psl.eu/evenement/tame-geometry-and-diophantine-approximation/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201016T090000
DTEND;TZID=Europe/Paris:20201016T102000
DTSTAMP:20261026T165845
CREATED:20201016T070000Z
LAST-MODIFIED:20211104T141431Z
UID:8556-1602838800-1602843600@www.math.ens.psl.eu
SUMMARY:Complex Cellular Structures
DESCRIPTION:Real semialgebraic sets admit so-called cellular decomposition\, i.e. representation as a union of convenient semialgebraic images of standard cubes.\nThe Gromov-Yomdin Lemma (later generalized by Pila and Wilkie) proves that the maps could be chosen of C^r-smooth norm at most one\, and the number of such maps is uniformly bounded for finite-dimensional families. This number was not effectively bounded by Yomdin or Gromov\, but itnecessarily grows as r ? ?.\nIt turns out there is a natural obstruction to a naive holomorphic complexification of this result related to the natural hyperbolic metric of complex holomorphic sets.\nWe prove a lemma about holomorphic functions in annulii\, a quantitative version of the great Picard theorem. This lemma allowed us to construct an effective holomorphic version of the cellular decomposition results in all dimensions\, with explicit polynomial bounds on complexity for families of complex (sub)analytic and semialgebraic sets.\nAs the first corollary we get an effective version of Yomdin-Gromov Lemma with polynomial bounds on the complexity\, thus proving a long-standing Yomdin conjecture about tail entropy of analytic maps.Further connection to diophantine applications will be explained in Gal’s talk.
URL:https://www.math.ens.psl.eu/evenement/complex-cellular-structures/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200306T170000
DTEND;TZID=Europe/Paris:20200306T182000
DTSTAMP:20261026T165845
CREATED:20200306T160000Z
LAST-MODIFIED:20211025T103821Z
UID:8545-1583514000-1583518800@www.math.ens.psl.eu
SUMMARY:Constructing pseudo-algebraically closed fields
DESCRIPTION:A field K is called pseudo-algebraically closed (PAC) if every absolutely irreducible variety defined over K has a K-rational point. These fields were introduced by Ax in his characterization of pseudo-finite fields and have since become an important object of study in both model theory and field arithmetic. We will explain how the analysis of a PAC field often reduces to questions about the model theory of the absolute group and describe how these reductions combine with a graph-coding construction of Cherlin\, van den Dries\, and Macintyre together with to construct PAC fields with prescribed combinatorial properties.
URL:https://www.math.ens.psl.eu/evenement/constructing-pseudo-algebraically-closed-fields/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200306T110000
DTEND;TZID=Europe/Paris:20200306T122000
DTSTAMP:20261026T165845
CREATED:20200306T100000Z
LAST-MODIFIED:20211025T103823Z
UID:8546-1583492400-1583497200@www.math.ens.psl.eu
SUMMARY:Some remarks on complex analytic functions in a definable context
DESCRIPTION:We fix an o-minimal expansion of the real field\, M say. Definabilitynotions are with respect to M. Let F = {f_x : x in X} be a definable familyof (single valued) complex analytic functions\, each one having domain somedisk\, D_x say\, in ?\, where the parameter space X is a definable subset of ?^mfor some m. We present some finiteness theorems for such families F whichare uniform in parameters and give some applications.We also speculate on the notion of “definable” Riemann surface.
URL:https://www.math.ens.psl.eu/evenement/some-remarks-on-complex-analytic-functions-in-a-definable-context/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200306T000000
DTEND;TZID=Europe/Paris:20200306T000000
DTSTAMP:20261026T165845
CREATED:20200305T230000Z
LAST-MODIFIED:20211025T103835Z
UID:8549-1583452800-1583452800@www.math.ens.psl.eu
SUMMARY:Exponential sums modulo powers of primes\, singularity theory\, and local global principles
DESCRIPTION:The theme of the talk is around the theory of Igusa’s local zeta functions\, his broader program on local global principles\, and recent progress on these via singularity theory and the minimal model program with M. Mustata and K. H. Nguyen. I will also present some new open questions that push Igusa’s program further\, and partial evidence obtained with K. H. Nguyen.
URL:https://www.math.ens.psl.eu/evenement/exponential-sums-modulo-powers-of-primes-singularity-theory-and-local-global-principles/
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200131T160000
DTEND;TZID=Europe/Paris:20200131T172000
DTSTAMP:20261026T165845
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:20261026T165845
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:20261026T165845
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:20191110T110000
DTEND;TZID=Europe/Paris:20191110T123000
DTSTAMP:20261026T165845
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:20261026T165845
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:20261026T165845
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:20261026T165845
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:20191011T160000
DTEND;TZID=Europe/Paris:20191011T173000
DTSTAMP:20261026T165845
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:20261026T165845
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:20191005T141500
DTEND;TZID=Europe/Paris:20191005T154500
DTSTAMP:20261026T165845
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:20190510T160000
DTEND;TZID=Europe/Paris:20190510T173000
DTSTAMP:20261026T165845
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:20261026T165845
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:20261026T165845
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
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190322T160000
DTEND;TZID=Europe/Paris:20190322T173000
DTSTAMP:20261026T165845
CREATED:20190322T150000Z
LAST-MODIFIED:20211104T141546Z
UID:8505-1553270400-1553275800@www.math.ens.psl.eu
SUMMARY:Patching over Berkovich Curves
DESCRIPTION:Patching was first introduced as an approach to the Inverse Galois Problem. The technique was then extended to a more algebraic setting and used to prove a local-global principle by D. Harbater\, J. Hartmann and D. Krashen. I will present an adaptation of the method of patching to the setting of Berkovich analytic curves. This will then be used to prove a local-global principle for function fields of curves that generalizes that of the above mentioned authors.
URL:https://www.math.ens.psl.eu/evenement/patching-over-berkovich-curves/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190322T000000
DTEND;TZID=Europe/Paris:20190322T000000
DTSTAMP:20261026T165845
CREATED:20190321T230000Z
LAST-MODIFIED:20211104T112226Z
UID:8501-1553212800-1553212800@www.math.ens.psl.eu
SUMMARY:Independence of CM points in elliptic curves
DESCRIPTION:I will speak about joint work with Jacob Tsimerman. Let E be an elliptic curve parameterized by a modular (or Shimura) curve. There are a number of results (…\, Buium-Poonen\, Kuhne) to the effect that the images of CM points are (under suitable hypotheses) linearly independent in E. We consider this issue in the setting of the Zilber-Pink conjecture and prove a result which improves previous results in some aspects
URL:https://www.math.ens.psl.eu/evenement/independence-of-cm-points-in-elliptic-curves/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190322T000000
DTEND;TZID=Europe/Paris:20190322T000000
DTSTAMP:20261026T165845
CREATED:20190321T230000Z
LAST-MODIFIED:20211104T112227Z
UID:8502-1553212800-1553212800@www.math.ens.psl.eu
SUMMARY:Counting rational points with the determinant method
DESCRIPTION:The determinant method gives upper bounds for the number of rational points of bounded height on or near algebraic varieties defined over global fields. There is a real-analytic version of the method due to Bombieri and Pila and a p-adic version due to Heath-Brown. The aim of our talk is to describe a global refinement of the p-adic method and some applications like a uniform bound for non-singular cubic curves which improves upon earlier bounds of Ellenberg-Venkatesh and Heath-Brown.
URL:https://www.math.ens.psl.eu/evenement/counting-rational-points-with-the-determinant-method/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190215T160000
DTEND;TZID=Europe/Paris:20190215T173000
DTSTAMP:20261026T165845
CREATED:20190215T150000Z
LAST-MODIFIED:20211104T111801Z
UID:8490-1550246400-1550251800@www.math.ens.psl.eu
SUMMARY:Definable subsets of a Berkovich curve
DESCRIPTION:Let k be an algebraically closed complete rank 1 non-trivially valued field. Let X be an algebraic curve over k and let X^an be its analytification in the sense of Berkovich. We functorially associate to X^an a definable set X^S in a natural language. As a corollary\, we obtain an alternative proof of a result of Hrushovski-Loeser about the iso-definability of curves. Our association being explicit allows us to provide a concrete description of the definable subsets of X^S: they correspond to radial sets. This is a joint work with Jérôme Poineau.
URL:https://www.math.ens.psl.eu/evenement/definable-subsets-of-a-berkovich-curve/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190215T141500
DTEND;TZID=Europe/Paris:20190215T154500
DTSTAMP:20261026T165845
CREATED:20190215T131500Z
LAST-MODIFIED:20211104T111802Z
UID:8492-1550240100-1550245500@www.math.ens.psl.eu
SUMMARY:Tame topology and Hodge theory.
DESCRIPTION:I will explain how tame topology seems the natural setting for variational Hodge theory. As an instance I will sketch a new proof of the algebraicity of the components of the Hodge locus\, a celebrated result of Cattani-Deligne-Kaplan (joint work with Bakker and Tsimerman).
URL:https://www.math.ens.psl.eu/evenement/tame-topology-and-hodge-theory/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190215T110000
DTEND;TZID=Europe/Paris:20190215T123000
DTSTAMP:20261026T165845
CREATED:20190215T100000Z
LAST-MODIFIED:20211104T111802Z
UID:8491-1550228400-1550233800@www.math.ens.psl.eu
SUMMARY:Unlikely intersections with E x CM curves in A_2
DESCRIPTION:The Zilber-Pink conjecture predicts that an algebraic curve in A_2 has only finitely many intersections with the special curves\, unless it is contained in a proper special subvariety.Under a large Galois orbits hypothesis\, we prove the finiteness of the intersection with the special curves parametrising abelian surfaces isogenous to the product of two elliptic curves\, at least one of which has complex multiplication. Furthermore\, we show that this large Galois orbits hypothesis holds for curves satisfying a condition on their intersection with the boundary of the Baily–Borel compactification of A_2.More generally\, we show that a Hodge generic curve in an arbitrary Shimura variety has only finitely many intersection points with the generic points of a so-called Hecke–facteur family\, again under a large Galois orbits hypothesis.This is a joint work with Martin Orr (University of Warwick).
URL:https://www.math.ens.psl.eu/evenement/unlikely-intersections-with-e-x-cm-curves-in-a_2/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
END:VCALENDAR