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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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TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20170326T010000
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TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20171029T010000
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TZNAME:CEST
DTSTART:20180325T010000
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DTSTART:20181028T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20181116T160000
DTEND;TZID=Europe/Paris:20181116T173000
DTSTAMP:20261026T194712
CREATED:20181116T150000Z
LAST-MODIFIED:20211104T111157Z
UID:8473-1542384000-1542389400@www.math.ens.psl.eu
SUMMARY:Oscillatory integrals of subanalytic functions
DESCRIPTION:In several papers\, R. Cluckers and D. Miller have built and investigated a class of real functions which contains the subanalytic functions and which is closed under parameterized integration. This class does not allow any oscillatory behavior\, nor stability under Fourier transform. On the other hand\, the behavior of oscillatory integrals\, in connection with singularity theory\, has been heavily investigated for decades. In this talk\, we explain how to build a class of complex functions\, which contains the subanalytic functions and their complex exponentials\, and which is closed under parameterized integration and under Fourier transform.Our techniques involve appropriate preparation theorems for subanalytic functions\, and some elements of the theory of uniformly distributed families of maps.(joint work with R. Clucker\, G. Comte\, D. Miller and T. Servi).
URL:https://www.math.ens.psl.eu/evenement/oscillatory-integrals-of-subanalytic-functions/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20181116T141500
DTEND;TZID=Europe/Paris:20181116T154500
DTSTAMP:20261026T194712
CREATED:20181116T131500Z
LAST-MODIFIED:20211104T110958Z
UID:8472-1542377700-1542383100@www.math.ens.psl.eu
SUMMARY:First-order logic in finitely generated fields
DESCRIPTION:The expressive power of first-order logic in the class of finitely generated fields\, as structures in the language of rings\, is relatively poorly understood. For instance\, Pop asked in 2002 whether elementarily equivalent finitely generated fields are necessarily isomorphic\, and this is still not known in the general case. On the other hand\, the related situation of finitely generated rings is much better understood by recent work of Aschenbrenner-Khélif-Naziazeno-Scanlon.Building on work of Pop and Poonen\, and using geometric results due to Kerz-Saito and Gabber\, I shall show that every infinite finitely generated field of characteristic not two admits a definable subring which is a finitely generated algebra over a global field. This implies that any such finitely generated field is biinterpretable with arithmetic\, and gives a positive answer to the question above in characteristic not two.
URL:https://www.math.ens.psl.eu/evenement/first-order-logic-in-finitely-generated-fields/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20181116T110000
DTEND;TZID=Europe/Paris:20181116T123000
DTSTAMP:20261026T194712
CREATED:20181116T100000Z
LAST-MODIFIED:20211104T110958Z
UID:8471-1542366000-1542371400@www.math.ens.psl.eu
SUMMARY:Non-standard analysis and non-archimedean geometry
DESCRIPTION:In this talk I will describe a joint work (still in progress) with E. Hrushovski and F. Loeser\, in which we explain how the integrals I have defined with Chambert-Loir on Berkovich spaces can beseen (in the t-adic case) as limits of usual integrals on complex algebraic varieties
URL:https://www.math.ens.psl.eu/evenement/non-standard-analysis-and-non-archimedean-geometry/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180518T160000
DTEND;TZID=Europe/Paris:20180518T173000
DTSTAMP:20261026T194712
CREATED:20180518T140000Z
LAST-MODIFIED:20211104T110740Z
UID:8460-1526659200-1526664600@www.math.ens.psl.eu
SUMMARY:Doubling parametrizations and Remez-type inequalities
DESCRIPTION:A doubling chart on an n-dimensional complex manifold Y is a univalent analytic mapping psi : B_1
URL:https://www.math.ens.psl.eu/evenement/doubling-parametrizations-and-remez-type-inequalities/
LOCATION:Jussieu salle 101 couloir 15-16 (1er étage)4 place Jussieu
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180518T141500
DTEND;TZID=Europe/Paris:20180518T154500
DTSTAMP:20261026T194712
CREATED:20180518T121500Z
LAST-MODIFIED:20211104T110741Z
UID:8461-1526652900-1526658300@www.math.ens.psl.eu
SUMMARY:Isotrivial Mordell-Lang and finite automata
DESCRIPTION:About fifteen years ago\, Thomas Scanlon and I gave a description of sets that arise as the intersection of a subvariety with a finitely generated subgroup inside a semiabelian variety over a finite field. Inspired by later work of Derksen on the positive characteristic Skolem-Mahler-Lech theorem\, which turns out to be a special case\, Jason Bell and I have recently recast those results in terms of finite automata. I will report on this work\, as well as on the work-in-progress it has engendered on an effective version of the isotrivial Mordell-Lang theorem.
URL:https://www.math.ens.psl.eu/evenement/isotrivial-mordell-lang-and-finite-automata/
LOCATION:Jussieu salle 101 couloir 15-16 (1er étage)4 place Jussieu
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180518T110000
DTEND;TZID=Europe/Paris:20180518T123000
DTSTAMP:20261026T194712
CREATED:20180518T090000Z
LAST-MODIFIED:20211104T110740Z
UID:8459-1526641200-1526646600@www.math.ens.psl.eu
SUMMARY:Groups and algebras
DESCRIPTION:To every group G is associated an associative algebra\, namely its group ring kG. Which (geometric) properties are reflected in (algebraic) properties of kG? I will survey some results and conjectures in this area\, concentrating on specific examples: growth\, amenability\, torsion\, and filtrations.
URL:https://www.math.ens.psl.eu/evenement/groups-and-algebras/
LOCATION:Jussieu salle 101 couloir 15-16 (1er étage)4 place Jussieu
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180323T160000
DTEND;TZID=Europe/Paris:20180323T173000
DTSTAMP:20261026T194712
CREATED:20180323T150000Z
LAST-MODIFIED:20211104T110539Z
UID:8455-1521820800-1521826200@www.math.ens.psl.eu
SUMMARY:A model theoretic generalization of the one-dimensional case of the Elekes-Szabo theorem
DESCRIPTION:(Joint work with A. Chernikov)Let V subseteq C^3 be a complex variety of dimension 2.The Elekes-Szabo Theorem says that if V contains `too many’ points on n x n x n Cartesian products then V has a special form: either V contains a cylinder over a curve or V is related to the graph of the multiplication of an algebraic group.In this talk we generalize the Elekes-Szabo Theorem to relations on strongly minimal sets interpretable in distal structures.
URL:https://www.math.ens.psl.eu/evenement/a-model-theoretic-generalization-of-the-one-dimensional-case-of-the-elekes-szabo-theorem/
LOCATION:IHP amphitheatre Darboux
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180323T141500
DTEND;TZID=Europe/Paris:20180323T154500
DTSTAMP:20261026T194712
CREATED:20180323T131500Z
LAST-MODIFIED:20211104T110538Z
UID:8453-1521814500-1521819900@www.math.ens.psl.eu
SUMMARY:The dynamical Mordell-Lang problem in positive characteristic
DESCRIPTION:The dynamical Mordell-Lang conjecture in characteristic zero predicts that if f : X –> X is a map of algebraic varieties over a field K of characteristic zero\, Y subset X is a closed subvariety and a in X(K) is a K-rational point on X\, then the return set { n in N : f^n(a) in Y(K) } is a finite union of points and arithmetic progressions. For K a field of characteristic p > 0\, it is necessary to allow for finite unions with sets of the form { a + sum_{i=1}^m p^{n_i} : (n_1\, … \, n_m) in N^m } and one might conjecture that all return sets are finite unions of points\, arithmetic progressions and such p-sets. We studied the special case of the positive characteristic dynamical Mordell-Lang problem on semiabelian varieites and using our earlier results with Moosa on so-called F-sets reduced the problem to that of solving a class of exponential diophantine equations in characteristic zero. In so doing\, under the hypothesis that X is a semiabelian variety and either Y has small dimension or f is sufficiently general\, we prove the conjecture. However\, we also show that our reduction to the exponential diiophantine problems may be reversed so that the positive characteristic dynamical Mordell-Lang conjecture in general is equivalent to a class of hard exponential diophantine problems which the experts consider to be out of reach given our present techniques. (This is a report on joint work with Pietro Corvaja\, Dragos Ghioca and Umberto Zannier available at arXiv:1802.05309.)
URL:https://www.math.ens.psl.eu/evenement/the-dynamical-mordell-lang-problem-in-positive-characteristic/
LOCATION:IHP amphitheatre Darboux
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180323T110000
DTEND;TZID=Europe/Paris:20180323T110000
DTSTAMP:20261026T194712
CREATED:20180323T100000Z
LAST-MODIFIED:20211104T110539Z
UID:8454-1521802800-1521802800@www.math.ens.psl.eu
SUMMARY:On a conjecture of Colliot-Thélène
DESCRIPTION:Let f be a morphism of projective smooth varieties X\, Y defined over the rationals. The conjecture by Colliot-Thélène under discussion gives (conjectural) sufficient conditions which imply that for almost all rational prime numbers p\, the map f maps the p-adic points X(Q_p) surjectively onto Y(Q_p). The aim of the talk is to present some recent results by Denef\, Skorobogatov et al
URL:https://www.math.ens.psl.eu/evenement/on-a-conjecture-of-colliot-thelene/
LOCATION:IHP amphitheatre Darboux
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180119T160000
DTEND;TZID=Europe/Paris:20180119T160000
DTSTAMP:20261026T194712
CREATED:20180119T150000Z
LAST-MODIFIED:20211104T105937Z
UID:8440-1516377600-1516377600@www.math.ens.psl.eu
SUMMARY:Blurred Complex Exponentiation
DESCRIPTION:Zilber conjectured that the complex field equipped with the exponential function is quasiminimal: every definable subset of the complex numbers is countable or co-countable. If true\, it would mean that the geometry of solution sets of complex exponential-polynomial equations and their projections is somewhat like algebraic geometry. If false\, it is likely that the real field is definable and there may be no reasonable geometric theory of these definable sets.I will report on some progress towards the conjecture\, including a proof when the exponential function is replaced by the approximate version given by exists q\,r in Q [y = e^{x+q+2pi i r}]. This set is the graph of the exponential function blurred by the group exp(Q + 2 pi i Q). We can also blur by a larger subgroup and prove a stronger version of the theorem. Not only do we get quasiminimality but the resulting structure is isomorphic to the analogous blurring of Zilber’s exponential field and to a reduct of a differentially closed field. Reference: Jonathan Kirby\, Blurred Complex Exponentiation\, arXiv:1705.04574
URL:https://www.math.ens.psl.eu/evenement/blurred-complex-exponentiation/
LOCATION:Amphitheatre Hermite IHP
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180119T141500
DTEND;TZID=Europe/Paris:20180119T141500
DTSTAMP:20261026T194712
CREATED:20180119T131500Z
LAST-MODIFIED:20211104T105936Z
UID:8439-1516371300-1516371300@www.math.ens.psl.eu
SUMMARY:Effective Chabauty and the Cursed Curve
DESCRIPTION:The Chabauty method often allows one to find the rational points on curves of genus at least 2 over the rationals\, but has a lot of limitations. On a theoretical level\, the Mordell-Weil rank of the Jacobian of the curve has to be strictly smaller than its genus. In practice\, even when this condition is satisfied\, the relevant Coleman integrals can usually only be computed for hyperelliptic curves. We will report on recent work of ours (with different combinations of collaborators) on extending the method to more general curves. In particular\, we will show how one can use an extension of the Chabauty method by Kim to find the rational points on the split Cartan modular curve of level 13\, which is also known as the cursed curve. The talk will be aimed at non-specialists with an interest in number theory.
URL:https://www.math.ens.psl.eu/evenement/effective-chabauty-and-the-cursed-curve/
LOCATION:Institut Henri Poincaré amphi Hermite
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180119T110000
DTEND;TZID=Europe/Paris:20180119T110000
DTSTAMP:20261026T194712
CREATED:20180119T100000Z
LAST-MODIFIED:20211104T105937Z
UID:8441-1516359600-1516359600@www.math.ens.psl.eu
SUMMARY:Spectral gap and definability
DESCRIPTION:Originating in the theory of unitary group representations\, the notion of spectral gap has played a huge role in many of the deep results in the theory of von Neumann algebras in the last couple of decades. Recently\, with my collaborators\, we are slowly understanding the model-theoretic significance of spectral gap\, in particular its connection with definability. In this talk\, I will discuss a few of our recent observations in this direction and speculate on some further possible developments. I will assume no knowledge of von Neumann algebras nor continuous logic. Various parts of this work are joint with Bradd Hart\, Thomas Sinclair\, and Henry Towsner.
URL:https://www.math.ens.psl.eu/evenement/spectral-gap-and-definability/
LOCATION:Amphitheatre Hermite IHP
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20171215T160000
DTEND;TZID=Europe/Paris:20171215T160000
DTSTAMP:20261026T194712
CREATED:20171215T150000Z
LAST-MODIFIED:20211104T105751Z
UID:8434-1513353600-1513353600@www.math.ens.psl.eu
SUMMARY:The geometry of combinatorially extreme algebraic configurations
DESCRIPTION:Given a system of polynomial equations in m complex variables with solution set of dimension d\, if we take finite subsets X_i of C each of size at most N\, then the number of solutions to the system whose ith co-ordinate is in X_i is easily seen to be bounded as O(N^d). We ask: when can we improve on the exponent d in this bound?Hrushovski developed a formalism in which such questions become amenable to the tools of model theory\, and in particular observed that incidence bounds of Szemeredi-Trotter type imply modularity of associated geometries. Exploiting this\, we answer a (more general form of) our question above. This is part of a joint project with Emmanuel Breuillard.
URL:https://www.math.ens.psl.eu/evenement/the-geometry-of-combinatorially-extreme-algebraic-configurations/
LOCATION:ENS. salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20171215T141500
DTEND;TZID=Europe/Paris:20171215T141500
DTSTAMP:20261026T194712
CREATED:20171215T131500Z
LAST-MODIFIED:20211104T105750Z
UID:8433-1513347300-1513347300@www.math.ens.psl.eu
SUMMARY:Géométrie des arcs et singularités
DESCRIPTION:Soulignée par Nash dans les années 60\, l’interaction entre la géométrie des espaces d’arcs et la théorie des singularités s’est fortement amplifiée sous l’influence de la théorie de l’intégration motivique notamment. Dans cet exposé\, nous introduirons le schéma des arcs associé à une variété algébrique et donnerons quelques illustrations de cette interaction. Parmi elles\, nous parlerons de l’interprétation (possible) du point de vue des singularités d’un théorème de Drinfeld et Grinberg-Kazhdan démontré au début des années 2000. (Cette dernière partie de l’exposé s’appuie sur une collaboration avec David Bourqui.)
URL:https://www.math.ens.psl.eu/evenement/geometrie-des-arcs-et-singularites/
LOCATION:ENS. salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20171215T110000
DTEND;TZID=Europe/Paris:20171215T110000
DTSTAMP:20261026T194712
CREATED:20171215T100000Z
LAST-MODIFIED:20211104T105553Z
UID:8432-1513335600-1513335600@www.math.ens.psl.eu
SUMMARY:On the conjecture of Ihara/Oda-Matsumoto
DESCRIPTION:Following the spirit of Grothendieck’s Esquisse d’un Programme\, the Ihara/Oda-Matsumoto conjecture predicted a combinatorial description of the absolute Galois group of Q based on its action on geometric fundamental groups of varieties. This conjecture was resolved in the 90’s by Pop using anabelian techniques. In this talk\, I will discuss the proof of stronger variant of this conjecture\, using mod-ell two-step nilpotent quotients\, while highlighting some connections with model theory.
URL:https://www.math.ens.psl.eu/evenement/on-the-conjecture-of-ihara-oda-matsumoto/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20171117T160000
DTEND;TZID=Europe/Paris:20171117T160000
DTSTAMP:20261026T194712
CREATED:20171117T150000Z
LAST-MODIFIED:20211104T105349Z
UID:8426-1510934400-1510934400@www.math.ens.psl.eu
SUMMARY:Quasi-minimal expansions of the complex field
DESCRIPTION:I discuss a back-and-forth technique for proving that in certain expansions of the complex field every L_{infty\, omega}-definable subset of C: is either countable or co-countable. Some successes of the method will also be discussed.
URL:https://www.math.ens.psl.eu/evenement/quasi-minimal-expansions-of-the-complex-field/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20171117T141500
DTEND;TZID=Europe/Paris:20171117T141500
DTSTAMP:20261026T194712
CREATED:20171117T131500Z
LAST-MODIFIED:20211104T105350Z
UID:8427-1510928100-1510928100@www.math.ens.psl.eu
SUMMARY:Incidence systems on Cartesian powers of algebraic curves
DESCRIPTION:The classical theory of abstract projective geometries establishes an equivalence between axiomatically defined incidence systems of points and lines and projective planes defined over a field. Zilber’s Restricted Trichotomy conjecture in dimension one is a generalization of this statement in a sense\, with lines replaced by algebraic curves
URL:https://www.math.ens.psl.eu/evenement/incidence-systems-on-cartesian-powers-of-algebraic-curves/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20171117T110000
DTEND;TZID=Europe/Paris:20171117T110000
DTSTAMP:20261026T194712
CREATED:20171117T100000Z
LAST-MODIFIED:20211104T105349Z
UID:8425-1510916400-1510916400@www.math.ens.psl.eu
SUMMARY:Sur les polynômes positifs qui sont sommes de peu de carrés
DESCRIPTION:Artin a résolu le 17ème problème de Hilbert : un polynôme réel positif en n variables est somme de carrés de fractions rationnelles. Pfister a amélioré ce résultat en démontrant qu’il est somme de 2^n carrés. Décider si la borne 2^n de Pfister est optimale est un problème ouvert si n>2. Nous expliquerons que cette borne peut être améliorée en petit degré et\, en deux variables\, pour un ensemble dense de polynômes positifs.
URL:https://www.math.ens.psl.eu/evenement/sur-les-polynomes-positifs-qui-sont-sommes-de-peu-de-carres/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20171013T160000
DTEND;TZID=Europe/Paris:20171013T173000
DTSTAMP:20261026T194712
CREATED:20171013T140000Z
LAST-MODIFIED:20211104T104931Z
UID:8411-1507910400-1507915800@www.math.ens.psl.eu
SUMMARY:Un nouvel analogue de l'o-minimalité dans des corps valués
DESCRIPTION:Pour les corps réel clos\, la notion d’o-minimalité a eu un énorme succès
URL:https://www.math.ens.psl.eu/evenement/un-nouvel-analogue-de-lo-minimalite-dans-des-corps-values/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20171013T141500
DTEND;TZID=Europe/Paris:20171013T154500
DTSTAMP:20261026T194712
CREATED:20171013T121500Z
LAST-MODIFIED:20211104T104930Z
UID:8409-1507904100-1507909500@www.math.ens.psl.eu
SUMMARY:Approximation\, domination and integration
DESCRIPTION:The talk will focus on results of two related strands of research undertaken by the speaker. The first is a model of quantum mechanics based on the idea of ‘structural approximation’. The earlier paper ‘The semantics of the canonical commutation relations’ (arxiv) established a method of calculation\, essentially integration\, for quantum mechanics with quadratic Hamiltonians. Currently\, we worked out a (model-theoretic) formalism for the method\, which allows us to perform more subtle calculations\, in particular\, we prove that our path integral calculation produce correct formula for quadratic Hamiltonians avoiding non-conventional limits used by physicists. Then we focus on the model-theoretic analysis of the notion of structural approximation and show that it can be seen as a positive model theory version of the theory of measurable structures\, compact domination and integration (p-adic and adelic).
URL:https://www.math.ens.psl.eu/evenement/approximation-domination-and-integration/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20171013T110000
DTEND;TZID=Europe/Paris:20171013T123000
DTSTAMP:20261026T194712
CREATED:20171013T090000Z
LAST-MODIFIED:20211104T105149Z
UID:8421-1507892400-1507897800@www.math.ens.psl.eu
SUMMARY:Corps globalement valués
DESCRIPTION:Dans un travail en commun avec E Hrushovski\, nous étudions les corps globalement valués\, qui sont une abstraction des corps de nombres\, de fonctions\, ou autres dans lesquels la formule du produit est vérifiée. Les questions habituelles de la théorie des modèles\, telle que l’existence d’une modèle-compagne ou encore sa stabilité\, nous mènent vers de nouvelles questions de nature plutôt géométrique.Je vais expliquer quelques avancées récentes dans ce sens\, où une analyse géométrique locale nous permet de déduire des propriété globales dans un corps globalement valués.
URL:https://www.math.ens.psl.eu/evenement/corps-globalement-values/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170519T160000
DTEND;TZID=Europe/Paris:20170519T160000
DTSTAMP:20261026T194712
CREATED:20170519T140000Z
LAST-MODIFIED:20211104T104256Z
UID:8385-1495209600-1495209600@www.math.ens.psl.eu
SUMMARY:Zéros et points rationnels des fonctions analytiques ou oscillant.
DESCRIPTION:Compter les points rationnels de hauteur bornée dans le graphe d’une fonction\, ou plus généralement d’une courbe (plane)\, se ramène à estimer le nombre Z_d de points d’intersection de cette courbe avec un ensemble algébrique de degré d donné. J’expliquerai     – d’une part comment on peut produire des familles de fonctions analytiques sur [0\,1] telle que Z_d est polynomialement borné en d\, et comment une telle borne assure que le graphe d’une telle fonction recèle moins de log?(T) points rationnels de hauteur < T\,      – d'autre part comment on peut traiter le cas de certaines courbes oscillant (ie non o-minimales) pour obtenir encore une borne du type log?(T). Il s'agit de travaux en commun avec Y. Yomdin d'une part et C. Miller d'autre part.
URL:https://www.math.ens.psl.eu/evenement/zeros-et-points-rationnels-des-fonctions-analytiques-ou-oscillant/
LOCATION:Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170519T141500
DTEND;TZID=Europe/Paris:20170519T141500
DTSTAMP:20261026T194712
CREATED:20170519T121500Z
LAST-MODIFIED:20211104T104256Z
UID:8384-1495203300-1495203300@www.math.ens.psl.eu
SUMMARY:Tame Expansions of o-minimal Structures
DESCRIPTION:Expanding a model theoretically `tame’ structure in a way that it stays `tame’ has been a theme in the recent years. In the first part of this talk\, we present a history of work done in that frame. Then we focus on the case of expansions of o-minimal structures by a unary predicate. There is a dividing line according to whether the predicate is dense or discrete
URL:https://www.math.ens.psl.eu/evenement/tame-expansions-of-o-minimal-structures/
LOCATION:Salle W ENS
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170519T110000
DTEND;TZID=Europe/Paris:20170519T110000
DTSTAMP:20261026T194712
CREATED:20170519T090000Z
LAST-MODIFIED:20211104T104256Z
UID:8383-1495191600-1495191600@www.math.ens.psl.eu
SUMMARY:Beyond o-minimality\, and why
DESCRIPTION:O-minimal structures on the real field have many desirable properties. As examples:     (a) Hausdorff (and even packing) dimension agrees with topological dimension on locally closed definable sets.    (b) Locally closed definable sets have few rational points (in the sense of the Pila-Wilkie Theorem).    (c) For each positive integer p\, every closed definable set is the zero set of a definable C^p function.    (d) Connected components of definable sets are definable.But to what extent is o-minimality necessary for these properties to hold? I will discuss this question\, and illustrate via examples as to why one might care about answers.
URL:https://www.math.ens.psl.eu/evenement/beyond-o-minimality-and-why/
LOCATION:Salle W ENS
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170428T160000
DTEND;TZID=Europe/Paris:20170428T160000
DTSTAMP:20261026T194712
CREATED:20170428T140000Z
LAST-MODIFIED:20211104T104241Z
UID:8380-1493395200-1493395200@www.math.ens.psl.eu
SUMMARY:Séries linéaires limites et applications
DESCRIPTION:Je présente un formalisme combinatoire pour l’étude des dégénérescences des séries linéaires dans une famille de courbes algébriques. J’en déduis quelques applications dont notamment l’équirépartition selon la mesure admissible de Zhang des points de ramification des fibrés en droite sur les courbes de Berkovich\, un analogue non-archimédien du théorème de Mumford-Neeman. Je discuterai aussi la question de la convergence de la mesure d’Arakelov vers la mesure de Zhang dans une famille de surfaces de Riemann.
URL:https://www.math.ens.psl.eu/evenement/series-lineaires-limites-et-applications/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170428T141500
DTEND;TZID=Europe/Paris:20170428T141500
DTSTAMP:20261026T194712
CREATED:20170428T121500Z
LAST-MODIFIED:20211104T104241Z
UID:8379-1493388900-1493388900@www.math.ens.psl.eu
SUMMARY:Triangulation des ensembles semi-algébriques p-adiques
DESCRIPTION:On sait que les ensembles semi-algébriques p-adiques admettent une décomposition cellulaire semblable à celle des semi-algébriques réels (Denef 1984). On sait aussi les classifier à bijection semi-algébrique près (Cluckers 2001)\, mais pas à homéomorphismes semi-algébriques près. En introduisant une notion appropriée de simplexe sur les corps p-adiquement clos\, on peut montrer que tout ensemble semi-algébrique p-adique est semi-algébriquement homéomorphe à un complexe simplicial p-adique\, exactement comme dans le cas réel clos. C’est ce résultat récent de `triangulation p-adique’ que je tâcherai de présenter\, avec ses applications les plus directes (existence de découpages avec contraintes aux bords\, existence de rétractions\, etc).
URL:https://www.math.ens.psl.eu/evenement/triangulation-des-ensembles-semi-algebriques-p-adiques/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170428T110000
DTEND;TZID=Europe/Paris:20170428T110000
DTSTAMP:20261026T194712
CREATED:20170428T090000Z
LAST-MODIFIED:20211104T104241Z
UID:8378-1493377200-1493377200@www.math.ens.psl.eu
SUMMARY:Un théorème d'Ax-Lindemann non-archimédien
DESCRIPTION:On présentera un résultat de type Ax-Lindemann pour les produits de courbes de Mumford sur un corps p-adique. Notre preuve reprend en l’adaptant les grandes lignes de l’approche de Pila dans le cas archimédien. En particulier nous utilisons un théorème de Pila-Wilkie p-adique obtenu avec R. Cluckers et G. Comte. Il s’agit d’un travail en commun avec A. Chambert-Loir.
URL:https://www.math.ens.psl.eu/evenement/un-theoreme-dax-lindemann-non-archimedien/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170310T160000
DTEND;TZID=Europe/Paris:20170310T160000
DTSTAMP:20261026T194712
CREATED:20170310T150000Z
LAST-MODIFIED:20211104T104002Z
UID:8368-1489161600-1489161600@www.math.ens.psl.eu
SUMMARY:Satellites of spherical subgroups and Poincaré polynomials
DESCRIPTION:Let G be a connected reductive group over C. One can associate with every spherical homogeneous space G/H its lattice of weights X^*(G/H) and a subset S of M of linearly independent primitive lattice vectors which are called the spherical roots. For any subset I of S we define\, up to conjugation\, a spherical subgroup H_I in G such that dim H_I = dim H and X^*(G/H_I) = X^*(G/H). We call the subgroups H_I the satellites of the spherical subgroup H. Our interest in satellites H_I is motivated by the space of arcs of the spherical homogeneous space G/H.We show a close relation between the Poincaré polynomials of the two spherical homogeneous spaces G/H and G/H_I.All of this is useful for the computation of the stringy E-function of Q-Gorenstein spherical embeddings.The talk is based on joint works with Victor Batyrev.
URL:https://www.math.ens.psl.eu/evenement/satellites-of-spherical-subgroups-and-poincare-polynomials/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170310T141500
DTEND;TZID=Europe/Paris:20170310T141500
DTSTAMP:20261026T194712
CREATED:20170310T131500Z
LAST-MODIFIED:20211104T104001Z
UID:8367-1489155300-1489155300@www.math.ens.psl.eu
SUMMARY:Quasianalytic Ilyashenko algebras
DESCRIPTION:In 1923\, Dulac published a proof of the claim that every real analytic vector field on the plane has only finitely many limit cycles (now known as Dulac’s Problem). In the mid-1990s\, Ilyashenko completed Dulac’s proof
URL:https://www.math.ens.psl.eu/evenement/quasianalytic-ilyashenko-algebras/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170310T110000
DTEND;TZID=Europe/Paris:20170310T110000
DTSTAMP:20261026T194712
CREATED:20170310T100000Z
LAST-MODIFIED:20211104T103601Z
UID:8361-1489143600-1489143600@www.math.ens.psl.eu
SUMMARY:Rational points on families of curves
DESCRIPTION:The TAC (torsion anomalous conjecture) states that for an irreducible variety V embedded transversaly in an abelian variety A there are only finitely many maximal V-torsion anomalous varieties. It is well know that the TAC implies the Mordell-Lang conjecture. S. Checcole\, F. Veneziano and myself were trying to prove some new cases of the TAC. In this process we realised that some methods could be made not only effective but even explicit. So we analysed the implication of this explicit methods on the Mordell Conjeture. Namely: can we make the Mordell Conjecture explicit for some new families of curves and so determine all the rational points on these curves? Of course we started with the easiest situation\, that is curves in ExE for E an elliptic curve. We eventually could give some new families of curves of growing genus for which we can determine all the rational points. I will explain the difficulties and the ingredients of this result. I will then discuss the generalisations of the method and also its limits.
URL:https://www.math.ens.psl.eu/evenement/rational-points-on-families-of-curves/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
END:VCALENDAR