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TZID:Europe/Paris
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DTSTART:20180325T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200131T141500
DTEND;TZID=Europe/Paris:20200131T153500
DTSTAMP:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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:20261026T175150
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
END:VCALENDAR