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:20190331T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20191027T010000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20200329T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20201025T010000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20210328T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20211031T010000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20220327T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20221030T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220121T154000
DTEND;TZID=Europe/Paris:20220121T171000
DTSTAMP:20261026T155909
CREATED:20220106T215337Z
LAST-MODIFIED:20220106T215337Z
UID:15010-1642779600-1642785000@www.math.ens.psl.eu
SUMMARY:Decidability via the tilting correspondence
DESCRIPTION:We discuss new decidability and undecidability results for mixed characteristic henselian fields\, whose proof goes via reduction to positive characteristic. The reduction uses extensively the theory of perfectoid fields and also the earlier Krasner-Kazhdan-Deligne principle. Our main results will be:\n(1) A relative decidability theorem for perfectoid fields. Using this\, we obtain decidability of certain tame fields of mixed characteristic.\n(2) An undecidability result for the asymptotic theory of all finite extensions of ℚ_p (fixed p) with cross-section.\nWe will also discuss a tentative step towards understanding the underlying model theory of arithmetic phenomena in this area\, by presenting a model-theoretic way of seeing the Fontaine-Wintenberger theorem
URL:https://www.math.ens.psl.eu/evenement/decidability-via-the-tilting-correspondence/
LOCATION:En ligne
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220121T140000
DTEND;TZID=Europe/Paris:20220121T153000
DTSTAMP:20261026T155909
CREATED:20220106T214555Z
LAST-MODIFIED:20220106T215523Z
UID:15001-1642773600-1642779000@www.math.ens.psl.eu
SUMMARY:Hensel minimality and counting in valued fields
DESCRIPTION:Hensel minimality is a new axiomatic framework for doing tame geometry in non-Archimedean fields\, aimed to mimic o-minimality. It is designed to be broadly applicable while having strong consequences. We will give a general overview of the theory of Hensel minimality. Afterwards\, we discuss arithmetic applications to counting rational points on definable sets in valued fields.\nThis is partially joint work with R. Cluckers\, I. Halupczok and S. Rideau-Kikuchi\, and partially with V. Cantoral-Farfan and K. Huu Nguyen.
URL:https://www.math.ens.psl.eu/evenement/hensel-minimality-and-counting-in-valued-fields/
LOCATION:En ligne
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20211202T090000
DTEND;TZID=Europe/Paris:20211202T120000
DTSTAMP:20261026T155909
CREATED:20211202T080000Z
LAST-MODIFIED:20211104T114114Z
UID:14115-1638435600-1638446400@www.math.ens.psl.eu
SUMMARY:On dp-finite fields
DESCRIPTION:Shelah’s conjecture predicts that any infinite NIP field iseither separably closed\, real closed or admits a non-trivial henselianvaluation. Recently\, Johnson proved that Shelah’s conjecture holds forfields of finite dp-rank\, also known as dp-finite fields. The aim of these two talks is to give an introduction to dp-rank in some algebraic structures and an overview of Johnson’s work.In the first talk\, we define dp-rank (which is a notion of rank in NIP theories) and give examples of dp-finite structures. In particular\, we discuss the dp-rank of ordered abelian groups and use them to construct multitude of examples of dp-finite fields. We also prove that every dp-finite field is perfect and sketch a proof that any valued field of dp-rank 1 is henselian.In the second talk\, we give an overview of Johnson’s proof that everyinfinite dp-finite field is either algebraically closed\, real closed oradmits a non-trivial henselian valuation. Crucially\, this relies on the notion of a W-topology\, a natural generalization of topologies arising from valuations\, and the construction of a definable W-topology on asufficiently saturated unstable dp-finite field.
URL:https://www.math.ens.psl.eu/evenement/on-dp-finite-fields-2/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210618T164000
DTEND;TZID=Europe/Paris:20210618T180000
DTSTAMP:20261026T155909
CREATED:20210618T144000Z
LAST-MODIFIED:20211104T140211Z
UID:8578-1624034400-1624039200@www.math.ens.psl.eu
SUMMARY:Real perspectives on monomialization.
DESCRIPTION:I will discuss recent work in collaboration with Edward Bierstone on transformation of a mapping to monomial form (with respect to local coordinates) by simple modifications of the source and target. Our techniques apply in a uniform way to the algebraic and analytic categories\, as well as to classes of infinitely differentiable real functions that are quasianalytic or definable in an o-minimal structure. Our results in the real cases are best possible. The talk will focus on real phenomena and on an application to quantifier elimination of certain o-minimal polynomially bounded structure.
URL:https://www.math.ens.psl.eu/evenement/real-perspectives-on-monomialization/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210618T150000
DTEND;TZID=Europe/Paris:20210618T162000
DTSTAMP:20261026T155909
CREATED:20210618T130000Z
LAST-MODIFIED:20211025T103955Z
UID:8577-1624028400-1624033200@www.math.ens.psl.eu
SUMMARY:Monadically NIP ordered graphs and bounded twin-width
DESCRIPTION:An open problem in theoretical computer science asks to characterize tameness for hereditary classes of finite structures. The notion of bounded twin-width was proposed and studied recently by Bonnet\, Geniet\, Kim\, Thommasé and Watrignant. Classes of graphs of bounded twin-width have many desirable properties. In particular\, they are monadically NIP (remain NIP after naming arbitrary unary predicates). In joint work with Szymon Torunczyk we show the converse for classes of ordered graphs. We then obtain a very clear dichotomy between tame (slow growth\, monadically NIP\, algorithmically simple …) and wild hereditary classes of ordered graphs. Those results were also obtained by Bonnet\, Giocanti\, Ossona de Mendez and Thomassé. In this talk\, I will focus on the model theoretic input.
URL:https://www.math.ens.psl.eu/evenement/monadically-nip-ordered-graphs-and-bounded-twin-width/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210521T103000
DTEND;TZID=Europe/Paris:20210521T115000
DTSTAMP:20261026T155909
CREATED:20210521T083000Z
LAST-MODIFIED:20211025T103953Z
UID:8576-1621593000-1621597800@www.math.ens.psl.eu
SUMMARY:Pseudo-T-closed fields\,  approximations and NTP2
DESCRIPTION:Joint work with Samaria MontenegroThe striking resemblance between the behaviour of pseudo-algebraically closed\, pseudo real closed and pseudo p-adically fields has lead to numerous attempts at describing their properties in a unified manner. In this talk I will present another of these attempts: the class of pseudo-T-closed fields\, where T is an enriched theory of fields. These fields verify a “local-global” principle with respect to models of T for the existence of points on varieties. Although it very much resembles previous such attempts\, our approach is more model theoretic in flavour\, both in its presentation and in the results we aim for.The first result I would like to present is an approximation result\, generalising a result of Kollar on PAC fields\, respectively Johnson on henselian fields. This result can be rephrased as the fact that existential closeness in certain topological enrichments come for free from existential closeness as a field. The second result is a (model theoretic) classification result for bounded pseudo-T-closed fields\, in the guise of the computation of their burden. One of the striking consequence of these two results is that a bounded perfect PAC field with n independent valuations has burden n and\, in particular\, is NTP2.
URL:https://www.math.ens.psl.eu/evenement/pseudo-t-closed-fields-approximations-and-ntp2/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210521T090000
DTEND;TZID=Europe/Paris:20210521T102000
DTSTAMP:20261026T155909
CREATED:20210521T070000Z
LAST-MODIFIED:20211104T140240Z
UID:8575-1621587600-1621592400@www.math.ens.psl.eu
SUMMARY:Curve-excluding fields
DESCRIPTION:Let T be the theory of fields K of characteristic 0 such that the equation x^4 + y^4 = 1 has only four solutions in K. We show that T has a model companion. More generally\, if K_0 is a field of characteristic 0 and C is a curve (affine or projective) of genus ≥ 2 with C(K_0) = ∅\, then there is a model companion CXF of the theory of fields K extending K_0 with C(K) = ∅.\nWe can use this theory to construct a field K with an interesting combination of properties. On the model-theoretic side\, the theory of K is complete\, decidable\, model-complete\, and algebraically bounded\, and K is a “geometric structure” in the sense of Hrushovski and Pillay. Additionally\, some classification-theoretic properties might hold in K. On the field-theoretic side\, K is non-large—there is a smooth curve C such that C(K) is finite and non-empty. This is unusual; the vast majority of model-theoretically tractable fields are large or finite. On the other hand\, K is “virtually large”—it has a finite extension which is large. In fact\, every proper algebraic extension of K is pseudo algebraically closed (PAC). The absolute Galois group of K is an ω-free profinite group. This negatively answers a question of Junker and Koenigsmann (is every model-complete infinite field large?) and a question of Macintyre (does every model-complete field have a small Galois group?).\nThis is based on joint work with Erik Walsberg and Vincent Ye.
URL:https://www.math.ens.psl.eu/evenement/curve-excluding-fields/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210423T163000
DTEND;TZID=Europe/Paris:20210423T175000
DTSTAMP:20261026T155909
CREATED:20210423T143000Z
LAST-MODIFIED:20211025T103942Z
UID:8573-1619195400-1619200200@www.math.ens.psl.eu
SUMMARY:Recognizing groups and fields in Erdős geometry and model theory
DESCRIPTION:Assume that Q is a relation on R^s of arity s definable in an o-minimal expansion of R. I will discuss how certain extremal asymptotic behaviors of the sizes of the intersections of Q with finite n  × … × n grids\, for growing n\, can only occur if Q is closely connected to a certain algebraic structure.On the one hand\, if the projection of Q onto any s-1 coordinates is finite-to-one but Q has maximal size intersections with some grids (of size >n^(s-1 – ε))\, then Q restricted to some open set is\, up to coordinatewise homeomorphisms\, of the form x_1+…+x_s=0. This is a special case of the recent generalization of the Elekes-Szabó theorem to any arity and dimension in which general abelian Lie groups arise (joint work with Kobi Peterzil and Sergei Starchenko).On the other hand\, if Q omits a finite complete s-partite hypergraph but can intersect finite grids in more that than n^(s-1 + ε) points\, then the real field can be definably recovered from Q (joint work with Abdul Basit\, Sergei Starchenko\, Terence Tao and Chieu-Minh Tran).I will explain how these results are connected to the model-theoretic trichotomy principle and discuss variants for higher dimensions\, and for stable structures with distal expansions.
URL:https://www.math.ens.psl.eu/evenement/recognizing-groups-and-fields-in-erds-geometry-and-model-theory/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210423T150000
DTEND;TZID=Europe/Paris:20210423T162000
DTSTAMP:20261026T155909
CREATED:20210423T130000Z
LAST-MODIFIED:20211104T140311Z
UID:8574-1619190000-1619194800@www.math.ens.psl.eu
SUMMARY:VC-dimension in model theory\, discrete geometry\, and combinatorics
DESCRIPTION:In statistical learning theory\, the notion of VC-dimension was developed by Vapnik and Chervonenkis in the context of approximating probabilities of events by the relative frequency of random test points. This notion has been widely used in combinatorics and computer science\, and is also directly connected to model theory through the study of NIP theories. This talk will start with an overview of VC-dimension\, with examples motivated by discrete geometry and additive combinatorics. I will then present several model theoretic applications of VC-dimension. The selection of topics will focus on the use of finitely approximable Keisler measures to analyze the structure of algebraic and combinatorial objects with bounded VC-dimension.
URL:https://www.math.ens.psl.eu/evenement/vc-dimension-in-model-theory-discrete-geometry-and-combinatorics/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210326T163000
DTEND;TZID=Europe/Paris:20210326T175000
DTSTAMP:20261026T155909
CREATED:20210326T153000Z
LAST-MODIFIED:20211025T103938Z
UID:8571-1616776200-1616781000@www.math.ens.psl.eu
SUMMARY:Linearization procedures in the semi-minimal analysis of algebraic differential equations
DESCRIPTION:It is well-known that certain algebraic differential equations restrain in an essential way the algebraic relations that their solutions share. For example\, the solutions of the first equation of Painlevé y » = 6y^2 + t are “new” transcendental functions of order two which whenever distinct are algebraically independent (together with their derivatives).I will first describe an account of such phenomena using the language of geometric stability theory in a differentially closed field. I will then explain how linearization procedures and geometric stability theory fit together to study such transcendence results in practice.
URL:https://www.math.ens.psl.eu/evenement/linearization-procedures-in-the-semi-minimal-analysis-of-algebraic-differential-equations/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210326T150000
DTEND;TZID=Europe/Paris:20210326T162000
DTSTAMP:20261026T155909
CREATED:20210326T140000Z
LAST-MODIFIED:20211104T140339Z
UID:8570-1616770800-1616775600@www.math.ens.psl.eu
SUMMARY:Effective isotrivial Mordell-Lang in positive characteristic
DESCRIPTION:The Mordell-Lang conjecture (now a theorem\, proved by Faltings\, Vojta\, McQuillan\,…) asserts that if G is a semiabelian variety G defined over an algebraically closed field of characteristic zero\, X is a subvariety of G\, and Γ is a finite rank subgroup of G\, then X ∩ Γ is a finite union of cosets of Γ. In positive characteristic\, the naive translation of this theorem does not hold\, however Hrushovski\, using model theoretic techniques\, showed that in some sense all counterexamples arise from semiabelian varieties defined over finite fields (the isotrivial case). This was later refined by Moosa and Scanlon\, who showed in the isotrivial case that the intersection of a subvariety of a semiabelian variety G with a finitely generated subgroup Γ of G that is invariant under the Frobenius endomorphism F: G → G is a finite union of sets of the form S+A\, where A is a subgroup of Γ and S is a sum of orbits under the map F. We show how how one can use finite-state automata to give a concrete description of these intersections Γ ∩ X in the isotrivial setting\, by constructing a finite machine that identifies all points in the intersection. In particular\, this allows us to give decision procedures for answering questions such as: is X ∩ Γ empty? finite? does it contain a coset of an infinite subgroup? In addition\, we are able to read off coarse asymptotic estimates for the number of points of height ≤ H in the intersection from the machine. This is joint work with Dragos Ghioca and Rahim Moosa.
URL:https://www.math.ens.psl.eu/evenement/effective-isotrivial-mordell-lang-in-positive-characteristic/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210115T111000
DTEND;TZID=Europe/Paris:20210115T123000
DTSTAMP:20261026T155909
CREATED:20210115T101000Z
LAST-MODIFIED:20211025T103926Z
UID:8567-1610709000-1610713800@www.math.ens.psl.eu
SUMMARY:Solving equations in finite groups and complete amalgamation
DESCRIPTION:Roth’s theorem on arithmetic progression states that a subset A of the natural numbers of positive upper density contains an arithmetic progression of length 3\, that is\, the equation x+z=2y has a solution in A.Finitary versions of Roth’s theorem study subsets A of {0\, … \, N}\, and ask whether the same holds for sufficiently large N\, for a fixed lower bound on the density. In a similar way\, concerning finite groups\, one may study whether or not sufficiently large sets of a finite group contain solutions of an equation\, or even a system of equations. For instance\, for the equation xy=z\, Gowers (2008) showed that any subset of a finite simple non-abelian group will contain many solutions to this equation\, provided it has sufficiently large density.We will report on recent work with Amador Martin-Pizarro on how to find solutions to the above equations in the context of pseudo-finite groups\, using techniques from model theory which resonate with (a group version of) the independence theorem in simple theories due to Pillay\, Scanlon and Wagner. In this talk\, we will not discuss the technical aspects of the proof\, but present the main ideas to a general audience.
URL:https://www.math.ens.psl.eu/evenement/solving-equations-in-finite-groups-and-complete-amalgamation/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210115T093000
DTEND;TZID=Europe/Paris:20210115T105000
DTSTAMP:20261026T155909
CREATED:20210115T083000Z
LAST-MODIFIED:20211025T103924Z
UID:8566-1610703000-1610707800@www.math.ens.psl.eu
SUMMARY:An application of surreal numbers to the asymptotic analysis of certain exponential functions
DESCRIPTION:Skolem (1956) studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant 1\, the identity function x\, and such that whenever f and g are in the set\, f+g\, fg and f^g are also in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz (1984) computed the order type of the fragment below 2^(2^x). They did so by studying the possible limits at infinity of the quotient f(x)/g(x) of two functions in the fragment: if g is kept fixed and f varies\, the possible limits form a discrete set of real numbers of order type omega.Using the surreal numbers\, we extend the latter result to the whole class of Skolem functions and we discuss some additional progress towards the conjecture of Skolem. This is joint work with Marcello Mamino (http://arxiv.org/abs/1911.07576\, to appear in the JSL).
URL:https://www.math.ens.psl.eu/evenement/an-application-of-surreal-numbers-to-the-asymptotic-analysis-of-certain-exponential-functions/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201211T090000
DTEND;TZID=Europe/Paris:20201211T102000
DTSTAMP:20261026T155909
CREATED:20201211T080000Z
LAST-MODIFIED:20211104T122913Z
UID:8563-1607677200-1607682000@www.math.ens.psl.eu
SUMMARY:Groups definable in o-minimal structures and algebraic groups
DESCRIPTION:Groups definable in o-minimal structures have been studied by many authors in the last 30 years and include algebraic groups over algebraically closed fields of characteristic 0\, semi-algebraic groups over real closed fields\, important classes of real Lie groups such as abelian groups\, compact groups and linear semisimple groups. In this talk I will present results on groups definable in o-minimal structures\, demonstrating a strong analogy with topological decompositions of linear algebraic groups. Limitations of this analogy will be shown through several examples.
URL:https://www.math.ens.psl.eu/evenement/groups-definable-in-o-minimal-structures-and-algebraic-groups/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201127T090000
DTEND;TZID=Europe/Paris:20201127T100000
DTSTAMP:20261026T155909
CREATED:20201127T080000Z
LAST-MODIFIED:20211104T141134Z
UID:8562-1606467600-1606471200@www.math.ens.psl.eu
SUMMARY:The étale-open topology (suite)
DESCRIPTION:Fix an abstract field K. For each K-variety V\, we will define an “étale-open” topology on the set V(K) of rational points of V. This notion uniformly recovers (1) the Zariski topology on V(K) when K is algebraically closed\, (2) the analytic topology on V(K) when K is the real numbers\, (3) the valuation topology on V(K) when K is almost any henselian field. On pseudo-finite fields\, the étale-open topology seems to be new\, and has some interesting properties.\nThe étale-open topology is mostly of interest when Kis large (also known as ample). On non-large fields\, theétale-open topology is discrete. In fact\, this propertycharacterizes largeness. Using this\, one can recover some well-knownfacts about large fields\, and classify the model-theoretically stablelarge fields. It may be possible to push these arguments towards aclassification of NIP large fields. Joint work with Chieu-Minh Tran\, Erik Walsberg\, and Jinhe Ye.
URL:https://www.math.ens.psl.eu/evenement/the-etale-open-topology-suite/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201113T103000
DTEND;TZID=Europe/Paris:20201113T115000
DTSTAMP:20261026T155909
CREATED:20201113T093000Z
LAST-MODIFIED:20211104T141149Z
UID:8559-1605263400-1605268200@www.math.ens.psl.eu
SUMMARY:Belles paires of valued fields and analytification
DESCRIPTION:In their work\, Hrushovski and Loeser proposed the space V̂ of generically stable types concentrating on V to study the homotopy type of the Berkovich analytification of V. An important feature of V̂ is that it is canonically identified as a projective limit of definable sets in ACVF\, which grants them tools from model theory. In this talk\, we will give a brief introduction to this object and present an alternative approach to internalize various spaces of definable types\, motivated by Poizat’s work on belles paires of stable theories. Several results of interest to model theorists will also be discussed. Particularly\, we recover the space V̂ is strict pro-definable and we propose a model-theoretic counterpart Ṽ of Huber’s analytification. Time permitting\, we will discuss some comparison and lifting results between V̂ and Ṽ. This is a joint project with Pablo Cubides Kovacsics and Martin Hils.
URL:https://www.math.ens.psl.eu/evenement/belles-paires-of-valued-fields-and-analytification/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201113T090000
DTEND;TZID=Europe/Paris:20201113T102000
DTSTAMP:20261026T155909
CREATED:20201113T080000Z
LAST-MODIFIED:20211104T141207Z
UID:8558-1605258000-1605262800@www.math.ens.psl.eu
SUMMARY:The étale-open topology
DESCRIPTION:Fix an abstract field K. For each K-variety V\, we will define an étale-open topology on the set V(K) of rational points of V. This notion uniformly recovers (1) the Zariski topology on V(K) when K is algebraically closed\, (2) the analytic topology on V(K) when K is the real numbers\, (3) the valuation topology on V(K) when K is almost any henselian field. On pseudo-finite fields\, the étale-open topology seems to be new\, and has some interesting properties.The étale-open topology is mostly of interest when K is large (also known as ample). On non-large fields\, the étale-open topology is discrete. In fact\, this property characterizes largeness. Using this\, one can recover some well-known facts about large fields\, and classify the model-theoretically stable large fields. It may be possible to push these arguments towards a classification of NIP large fields. Joint work with Chieu-Minh Tran\, Erik Walsberg\, and Jinhe Ye.
URL:https://www.math.ens.psl.eu/evenement/the-etale-open-topology/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201112T103000
DTEND;TZID=Europe/Paris:20201112T115000
DTSTAMP:20261026T155909
CREATED:20201112T093000Z
LAST-MODIFIED:20211104T121624Z
UID:14111-1605177000-1605181800@www.math.ens.psl.eu
SUMMARY:Cohomology of algebraic varieties over non-archimedean fields
DESCRIPTION:I will report on a joint work with Mário Edmundo and Jinhe Ye in which we introduced a sheaf cohomology theory for algebraic varieties over non-archimedean fields based on Hrushovski-Loeser spaces. After informally framing our main results with respect to classical statements\, I will discuss some details of our construction and the main difficulties arising in this new context. If time allows\, I will further explain how our results allow us to recover results of V. Berkovich on the sheaf cohomology of the analytification of an algebraic variety over a rank 1 complete non-archimedean field.
URL:https://www.math.ens.psl.eu/evenement/cohomology-of-algebraic-varieties-over-non-archimedean-fields-2/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201016T103000
DTEND;TZID=Europe/Paris:20201016T115000
DTSTAMP:20261026T155909
CREATED:20201016T083000Z
LAST-MODIFIED:20211104T141411Z
UID:8557-1602844200-1602849000@www.math.ens.psl.eu
SUMMARY:Tame geometry and diophantine approximation
DESCRIPTION:Tame geometry is the study of structures where the definable sets admit finite complexity. Around 15 years ago Pila and Wilkie discovered a deep connection between tame geometry and diophantine approximation\, in the form of asymptotic estimates on the number of rational points in a tame set (as a function of height). This later led to deep applications in diophantine geometry\, functional transcendence and Hodge theory.I will describe some conjectures and a long-term project around a more effective form of tame geometry\, suited for improving the quality of the diophantine approximation results and their applications. I will try to outline some of the pieces that are already available\, and how they should conjecturally fit together. Finally I will survey some applications of the existing results around the Manin-Mumford conjecture\, the Andre-Oort conjecture\, Galois-orbit lower bounds in Shimura varieties\, unlikely intersections in group schemes\, and some other directions (time permitting).
URL:https://www.math.ens.psl.eu/evenement/tame-geometry-and-diophantine-approximation/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201016T090000
DTEND;TZID=Europe/Paris:20201016T102000
DTSTAMP:20261026T155909
CREATED:20201016T070000Z
LAST-MODIFIED:20211104T141431Z
UID:8556-1602838800-1602843600@www.math.ens.psl.eu
SUMMARY:Complex Cellular Structures
DESCRIPTION:Real semialgebraic sets admit so-called cellular decomposition\, i.e. representation as a union of convenient semialgebraic images of standard cubes.\nThe Gromov-Yomdin Lemma (later generalized by Pila and Wilkie) proves that the maps could be chosen of C^r-smooth norm at most one\, and the number of such maps is uniformly bounded for finite-dimensional families. This number was not effectively bounded by Yomdin or Gromov\, but itnecessarily grows as r ? ?.\nIt turns out there is a natural obstruction to a naive holomorphic complexification of this result related to the natural hyperbolic metric of complex holomorphic sets.\nWe prove a lemma about holomorphic functions in annulii\, a quantitative version of the great Picard theorem. This lemma allowed us to construct an effective holomorphic version of the cellular decomposition results in all dimensions\, with explicit polynomial bounds on complexity for families of complex (sub)analytic and semialgebraic sets.\nAs the first corollary we get an effective version of Yomdin-Gromov Lemma with polynomial bounds on the complexity\, thus proving a long-standing Yomdin conjecture about tail entropy of analytic maps.Further connection to diophantine applications will be explained in Gal’s talk.
URL:https://www.math.ens.psl.eu/evenement/complex-cellular-structures/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200306T170000
DTEND;TZID=Europe/Paris:20200306T182000
DTSTAMP:20261026T155909
CREATED:20200306T160000Z
LAST-MODIFIED:20211025T103821Z
UID:8545-1583514000-1583518800@www.math.ens.psl.eu
SUMMARY:Constructing pseudo-algebraically closed fields
DESCRIPTION:A field K is called pseudo-algebraically closed (PAC) if every absolutely irreducible variety defined over K has a K-rational point. These fields were introduced by Ax in his characterization of pseudo-finite fields and have since become an important object of study in both model theory and field arithmetic. We will explain how the analysis of a PAC field often reduces to questions about the model theory of the absolute group and describe how these reductions combine with a graph-coding construction of Cherlin\, van den Dries\, and Macintyre together with to construct PAC fields with prescribed combinatorial properties.
URL:https://www.math.ens.psl.eu/evenement/constructing-pseudo-algebraically-closed-fields/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200306T110000
DTEND;TZID=Europe/Paris:20200306T122000
DTSTAMP:20261026T155909
CREATED:20200306T100000Z
LAST-MODIFIED:20211025T103823Z
UID:8546-1583492400-1583497200@www.math.ens.psl.eu
SUMMARY:Some remarks on complex analytic functions in a definable context
DESCRIPTION:We fix an o-minimal expansion of the real field\, M say. Definabilitynotions are with respect to M. Let F = {f_x : x in X} be a definable familyof (single valued) complex analytic functions\, each one having domain somedisk\, D_x say\, in ?\, where the parameter space X is a definable subset of ?^mfor some m. We present some finiteness theorems for such families F whichare uniform in parameters and give some applications.We also speculate on the notion of “definable” Riemann surface.
URL:https://www.math.ens.psl.eu/evenement/some-remarks-on-complex-analytic-functions-in-a-definable-context/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200306T000000
DTEND;TZID=Europe/Paris:20200306T000000
DTSTAMP:20261026T155909
CREATED:20200305T230000Z
LAST-MODIFIED:20211025T103835Z
UID:8549-1583452800-1583452800@www.math.ens.psl.eu
SUMMARY:Exponential sums modulo powers of primes\, singularity theory\, and local global principles
DESCRIPTION:The theme of the talk is around the theory of Igusa’s local zeta functions\, his broader program on local global principles\, and recent progress on these via singularity theory and the minimal model program with M. Mustata and K. H. Nguyen. I will also present some new open questions that push Igusa’s program further\, and partial evidence obtained with K. H. Nguyen.
URL:https://www.math.ens.psl.eu/evenement/exponential-sums-modulo-powers-of-primes-singularity-theory-and-local-global-principles/
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200131T160000
DTEND;TZID=Europe/Paris:20200131T172000
DTSTAMP:20261026T155909
CREATED:20200131T150000Z
LAST-MODIFIED:20211025T103757Z
UID:8538-1580486400-1580491200@www.math.ens.psl.eu
SUMMARY:Geometric quadratic Chabauty.
DESCRIPTION:Determining all rational points on a curve of genus at least 2 can be difficult. Chabauty’s method (1941) is to intersect\, for a prime number p\, in the p-adic Lie group of p-adic points of the jacobian\, the closure of the Mordell-Weil group with the p-adic points of the curve. If the Mordell-Weil rank is less than the genus then this method has never failed. Minhyong Kim’s non-abelian Chabauty programme aims to remove the condition on the rank. The simplest case\, called quadratic Chabauty\, was developed by Balakrishnan\, Dogra\, Mueller\, Tuitman and Vonk\, and applied in a tour de force to the so-called cursed curve (rank and genus both 3). This article aims to make the quadratic Chabauty method small and geometric again\, by describing it in terms of only `simple algebraic geometry’ (line bundles over the jacobian and models over the integers).
URL:https://www.math.ens.psl.eu/evenement/geometric-quadratic-chabauty/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200131T141500
DTEND;TZID=Europe/Paris:20200131T153500
DTSTAMP:20261026T155909
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:20261026T155909
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:20261026T155909
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:20261026T155909
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:20261026T155909
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:20261026T155909
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
END:VCALENDAR