BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20170326T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20171029T010000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20180325T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20181028T010000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20190331T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20191027T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190322T160000
DTEND;TZID=Europe/Paris:20190322T173000
DTSTAMP:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190111T160000
DTEND;TZID=Europe/Paris:20190111T173000
DTSTAMP:20261026T184256
CREATED:20190111T150000Z
LAST-MODIFIED:20211104T111600Z
UID:8484-1547222400-1547227800@www.math.ens.psl.eu
SUMMARY:Tame open core and small groups in pairs of topological geometric structures
DESCRIPTION:Using the group configuration theorem\, Hrushovski and Pillay showed that the law of a group definable in the reals or the p-adics is locally an algebraic group law\, up to definable isomorphism. There are some natural expansions of these two theories of fields\, by adding a predicate for a dense substructure\, for example the algebraic reals or the algebraic p-adics. We will present an overview on some of the features of these expansions\, and particularly on the characterisation of open definable sets as well as of groups definable in the pairs.
URL:https://www.math.ens.psl.eu/evenement/tame-open-core-and-small-groups-in-pairs-of-topological-geometric-structures/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190111T141500
DTEND;TZID=Europe/Paris:20190111T154500
DTSTAMP:20261026T184256
CREATED:20190111T131500Z
LAST-MODIFIED:20211104T111400Z
UID:8482-1547216100-1547221500@www.math.ens.psl.eu
SUMMARY:Definability in the infinitesimal subgroup of a simple compact Lie group
DESCRIPTION:Joint work with Kobi Peterzil.Let G be a simple compact Lie group\, for example G=SO_3(R). We consider the structure of definable sets in the subgroup G^{00} of infinitesimal elements. In an aleph_0-saturated elementary extension of the real field\, G^{00} is the inverse image of the identity under the standard part map\, so is definable in the corresponding valued field. We show that the pure group structure on G^{00} recovers the valued field\, making this a bi-interpretation. Hence the definable sets in the group are as rich as possible.
URL:https://www.math.ens.psl.eu/evenement/definability-in-the-infinitesimal-subgroup-of-a-simple-compact-lie-group/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190111T110000
DTEND;TZID=Europe/Paris:20190111T123000
DTSTAMP:20261026T184256
CREATED:20190111T100000Z
LAST-MODIFIED:20211104T111559Z
UID:8483-1547204400-1547209800@www.math.ens.psl.eu
SUMMARY:Scrollar invariants\, resolvents\, and syzygies
DESCRIPTION:With every cover C -> P^1 of the projective line one can associate its so-called scrollar invariants (also called Maroni invariants) which describe how the push-forward of the structure sheaf of C splits over P^1. They can be viewed as geometric counterparts of the successive minima of the lattice associated with the ring of integers of a number field. In this talk we consider the following problem: how do the scrollar invariants of the Galois closure C’ -> P^1 and of its various subcovers (the so-called resolvents of C -> P^1) relate to known invariants of the given cover? This concerns ongoing work with Yongqiang Zhao\, in which we put a previous observation for covers of degree 4 due to Casnati in a more general framework. As we will see the answer involves invariants related to syzygies that were introduced by Schreyer. As time permits\, we will discuss a number-theoretic manifestation of the phenomena observed.
URL:https://www.math.ens.psl.eu/evenement/scrollar-invariants-resolvents-and-syzygies/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20181214T160000
DTEND;TZID=Europe/Paris:20181214T173000
DTSTAMP:20261026T184256
CREATED:20181214T150000Z
LAST-MODIFIED:20211104T111159Z
UID:8477-1544803200-1544808600@www.math.ens.psl.eu
SUMMARY:On differentially large fields.
DESCRIPTION:Recall that a field K is large if it is existentially closed in K((t)). Examples of such fields are the complex\, the real\, and the p-adic numbers. This class of fields has been exploited significantly by F. Pop and others in inverse Galois-theoretic problems. In recent work with M. Tressl we introduced and explored a differential analogue of largeness\, that we conveniently call « differentially large ». I will present some properties of such fields\, and use a twisted version of the Taylor morphism to characterise them using formal Laurent series and to even construct « natural » examples (which ultimately yield examples of DCFs and CODFs… acronyms that will be explained in the talk).
URL:https://www.math.ens.psl.eu/evenement/on-differentially-large-fields/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20181214T110000
DTEND;TZID=Europe/Paris:20181214T123000
DTSTAMP:20261026T184256
CREATED:20181214T100000Z
LAST-MODIFIED:20211104T111358Z
UID:8478-1544785200-1544790600@www.math.ens.psl.eu
SUMMARY:Uniform bound for points of bounded degree in function fields of positive characteristic
DESCRIPTION:I will present a bound for the number of F_q[t]-points of bounded degree in a variety defined over Z[t]\, uniform in q. This generalizes work by Sedunova for fixed q. The proof involves model theory of valued fields with algebraic Skolem functions and uniform non-Archimedean Yomdin-Gromov parametrizations. This is joint work with Raf Cluckers and François Loeser.
URL:https://www.math.ens.psl.eu/evenement/uniform-bound-for-points-of-bounded-degree-in-function-fields-of-positive-characteristic/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20181213T141500
DTEND;TZID=Europe/Paris:20181213T154500
DTSTAMP:20261026T184256
CREATED:20181213T131500Z
LAST-MODIFIED:20211104T111359Z
UID:8480-1544710500-1544715900@www.math.ens.psl.eu
SUMMARY:Ax-Lindemann-Weierstrass with derivatives and the genus 0 Fuchsian groups
DESCRIPTION:We prove the Ax-Lindemann-Weierstrass theorem for the uniformizing functions of genus zero Fuchsian groups of the first kind. Our proof relies on differential Galois theory of Schwarzian equations and machinery from the model theory of differentially closed fields. This result generalizes previous work of Pila-Tsimerman on the j function. (Joint work with James Freitag and Joel Nagloo)
URL:https://www.math.ens.psl.eu/evenement/ax-lindemann-weierstrass-with-derivatives-and-the-genus-0-fuchsian-groups/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20181116T160000
DTEND;TZID=Europe/Paris:20181116T173000
DTSTAMP:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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:20261026T184256
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
END:VCALENDAR