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X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210423T163000
DTEND;TZID=Europe/Paris:20210423T175000
DTSTAMP:20260418T212529
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:20260418T212529
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:20210330T140000
DTEND;TZID=Europe/Paris:20210330T170000
DTSTAMP:20260418T212529
CREATED:20210330T120000Z
LAST-MODIFIED:20211108T205327Z
UID:8572-1617112800-1617123600@www.math.ens.psl.eu
SUMMARY:Après-midi de marches aléatoires et des groupes moyennables
DESCRIPTION:Zoom: https://us02web.zoom.us/j/85927181837\nMot de passe: G est un Graphe de Cayley du groupe libre à 107 générateurs. Quel est le degré de ce graphe?\nTapez le numéro à trois chiffres comme un mot de passe. \n\n14.00 – 14.45 Hanna Oppelmayer\, Random walks on dense subgroups of totally disconnected locally compact groups\n15.00 – 15.45 Georgii Veprev\, Non-existence of a universal zero entropy system for non-periodic amenable group actions\n16.15 – 17.00 Paul-Henry Leemann\, De Bruijn graphs\, spider web graphs and Lamplighter groups
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-marches-aleatoires-et-des-groupes-moyennables/
LOCATION:Zoom: https://us02web.zoom.us/j/85927181837
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210326T163000
DTEND;TZID=Europe/Paris:20210326T175000
DTSTAMP:20260418T212529
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:20260418T212529
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:20210119T160000
DTEND;TZID=Europe/Paris:20210119T190000
DTSTAMP:20260418T212529
CREATED:20210119T150000Z
LAST-MODIFIED:20211104T134537Z
UID:8569-1611072000-1611082800@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:Zoom: https://us02web.zoom.us/j/84778703586Mot de passe: G est un Graphe de Cayley du groupe libre à 107 générateurs. Quel est le degré de ce graphe? Tapez le numéro à trois chiffres comme un mot de passe.16.00-16.45 Igor Pak\, Cogrowth sequences in groups and graphs17.00-17.45 Behrang Forghani\, Boundary Preserving Transformations18.15-19.00 Mehrdad Kalantar\, On weak containment properties of quasi-regular representations of stabilizer subgroups of boundary actions
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-12/
LOCATION:Zoom: https://us02web.zoom.us/j/84778703586
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210115T111000
DTEND;TZID=Europe/Paris:20210115T123000
DTSTAMP:20260418T212529
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:20260418T212529
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:20260418T212529
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:20201208T150000
DTEND;TZID=Europe/Paris:20201208T180000
DTSTAMP:20260418T212529
CREATED:20201208T140000Z
LAST-MODIFIED:20211104T133753Z
UID:8565-1607439600-1607450400@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:Zoom: https://us02web.zoom.us/j/82502264227The password is answer to the following question: What is the degree of the standard Cayely graph on 107 generators?15.00-15.45 Robert Young (NYY Courant and IAS Princeton)\, Holder maps to the Heisenberg group16.00-16.45 Matei Coiculescu (Brown University)\, The Spheres of Sol17.15-18.00 Richard Schwartz (Brown University and IAS Princeton)\, The areas of metric spheres in Sol
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-11/
LOCATION:Zoom: https://us02web.zoom.us/j/82502264227
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201127T090000
DTEND;TZID=Europe/Paris:20201127T100000
DTSTAMP:20260418T212529
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:20201124T140000
DTEND;TZID=Europe/Paris:20201124T170000
DTSTAMP:20260418T212529
CREATED:20201124T130000Z
LAST-MODIFIED:20211104T134624Z
UID:8561-1606226400-1606237200@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:https://us02web.zoom.us/j/83180342864The password is answer to the following question: What is the degree of the standard Cayely graph on 107 generators?14.00-14.45 Alessandro Sisto (Heriot-Watt)\, Cubulation of hulls and bicombings15.00-15.45 Thomas Haettel (Montpellier)\, The coarse Helly property\, hierarchical hyperbolicity and semihyperbolicity16.15-17.00 Mark Hagen (Bristol)\, Wallspaces\, the Behrstock inequality\, and l_1 metrics onasymptotic cones
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-10/
LOCATION:Zoom: https://us02web.zoom.us/j/83180342864
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201113T103000
DTEND;TZID=Europe/Paris:20201113T115000
DTSTAMP:20260418T212529
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:20260418T212529
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:20260418T212529
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:20201027T090000
DTEND;TZID=Europe/Paris:20201027T120000
DTSTAMP:20260418T212529
CREATED:20201027T080000Z
LAST-MODIFIED:20211104T134742Z
UID:8560-1603789200-1603800000@www.math.ens.psl.eu
SUMMARY:Une matinée de théorie de groupes
DESCRIPTION:https://us02web.zoom.us/j/86850693514The password is answer to the following question: What is the degree of the standard Cayely graph on 107 generators?09.00-09.45 Koji Fujiwara (Kyoto)\, The rates of growth in a hyperbolic group10.00-10.45 Macarena Arenas (Cambridge)\, Linear isoperimetric functions for surfaces in hyperbolic groups11.15-12.00 Indira Chatterji (Nice)\, Tangent bundles on hyperbolic spaces and proper actions on Lp spaces
URL:https://www.math.ens.psl.eu/evenement/une-matinee-de-theorie-de-groupes/
LOCATION:Zoom: https://us02web.zoom.us/j/86850693514
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201016T103000
DTEND;TZID=Europe/Paris:20201016T115000
DTSTAMP:20260418T212529
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:20260418T212529
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:20200324T160000
DTEND;TZID=Europe/Paris:20200324T173000
DTSTAMP:20260418T212529
CREATED:20200324T150000Z
LAST-MODIFIED:20211025T103827Z
UID:8548-1585065600-1585071000@www.math.ens.psl.eu
SUMMARY:Ensembles IP et ultraproduits de groupes finis
DESCRIPTION:Une sous-partie d’un groupe infini est IP si elle contient tous les produits finis (sans répétitions) d’un sous-ensemble infini. Le célèbre théorème de Hindman affirme que\, pour toute coloration finie des entiers positifs\, il existe un ensemble IP monochromatique. Au delà du cas abélien\, Bergelson et Tao ont repris un travail de Gowers pour montrer qu’une sous-partie `large’ dans un ultraproduit de groupes finis simples non-abéliens est IP.Dans un travail en commun avec D. Palacin (Freiburg)\, nous allons donner dans cet exposé une démonstration alternative du résultat précédent\, avec des techniques modèles-théoriques élémentaires.
URL:https://www.math.ens.psl.eu/evenement/ensembles-ip-et-ultraproduits-de-groupes-finis/
LOCATION:Sophie Germain Salle 2020
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200310T000000
DTEND;TZID=Europe/Paris:20200310T000000
DTSTAMP:20260418T212529
CREATED:20200309T230000Z
LAST-MODIFIED:20211025T103825Z
UID:8547-1583798400-1583798400@www.math.ens.psl.eu
SUMMARY:Théories non-équationnelles
DESCRIPTION:Une théorie est équationnelle\, si toute formule est combination booléenne d’équations. Une équation est une formule telle que la famille d’intersections finies d’instances n’admet aucune chaine infinie décroissante. Toute théorie équationnelle est stable\, mais la réciproque n’est pas vraie : Sela ainsi que Müller-Sklinos ont montré que le groupe libre non-abélien n’est pas équationnel. Malgré tout\, on connaît peu d’exemples de théories stables non-équationnelles.Dans cet exposé\, nous présenterons un travail en commun avec Martin Ziegler\, où nous exhiberons une infinité de nouvelles théories stables non-équationnelles\, à partir du pseudo-espace coloré de Hrushovski et Srour.
URL:https://www.math.ens.psl.eu/evenement/theories-non-equationnelles/
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200306T170000
DTEND;TZID=Europe/Paris:20200306T182000
DTSTAMP:20260418T212529
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:20260418T212529
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:20260418T212529
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:20200303T160000
DTEND;TZID=Europe/Paris:20200303T173000
DTSTAMP:20260418T212529
CREATED:20200303T150000Z
LAST-MODIFIED:20211104T113418Z
UID:8544-1583251200-1583256600@www.math.ens.psl.eu
SUMMARY:Les décompositions paradoxales et les théories simples
DESCRIPTION:Y-a-t-il une théorie des mesures de Keisler pour les théories simples? J’expliquerai quelques exemples\, suggérés par Hrushovski\, qui montrent que les mesures dans une théorie simple sont plus complexes que prévu. Ils sont basés sur des actions de groupes libres.Travail en commun avec plusieurs chercheurs.
URL:https://www.math.ens.psl.eu/evenement/les-decompositions-paradoxales-et-les-theories-simples/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200225T160000
DTEND;TZID=Europe/Paris:20200225T173000
DTSTAMP:20260418T212529
CREATED:20200225T150000Z
LAST-MODIFIED:20211025T103813Z
UID:8543-1582646400-1582651800@www.math.ens.psl.eu
SUMMARY:Autour d'un théorème d'approximation d'Artin
DESCRIPTION:(avec Tom Scanlon)J’exposerai un résultat d’élimination des quantificateurs pour les corps henséliens de degré d’imperfection fini\, relativement à la famille uniforme de tous les groupes RV_gamma = K^\,imes/1+gamma m. Ce résultat permet alors de démontrer que toute extension dense séparable de corps henséliens de même degré d’imperfection fini est élémentaire. En particulier\, l’extension F_p(t)^h leq  F_p((t)) est élémentaire. Ce dernier énoncé précise un résultat d’Artin selon lequel elle est existentiellement close.
URL:https://www.math.ens.psl.eu/evenement/autour-dun-theoreme-dapproximation-dartin/
LOCATION:Salle 2015 Sophie Germain
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200218T150000
DTEND;TZID=Europe/Paris:20200218T170000
DTSTAMP:20260418T212529
CREATED:20200218T140000Z
LAST-MODIFIED:20211104T134933Z
UID:8542-1582038000-1582045200@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00-14.45 David Hume (Oxford)\, Three dichotomies for connected unimodular Lie groups15.00-15.45 Nikolay Bogachev (Skoltech & MIPT)\, Arithmetic hyperbolic reflection groups16.15-17.00 Daniel Woodhouse (Oxford)\, Action rigidity of free products of hyperbolic manifold groups
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-9/
LOCATION:Salle W (DMA ENS)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200131T160000
DTEND;TZID=Europe/Paris:20200131T172000
DTSTAMP:20260418T212529
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:20260418T212529
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:20260418T212529
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:20200121T150000
DTEND;TZID=Europe/Paris:20200121T170000
DTSTAMP:20260418T212529
CREATED:20200121T140000Z
LAST-MODIFIED:20211104T135010Z
UID:8539-1579618800-1579626000@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:14.00-14.45 Francois Dahmani (Grenoble)\, Relative hyperbolicity of free-by-cyclic groups\, and conjugacy between automorphisms of free groups15.00-15.45 Tatiana Smirnova-Nagnibeda (Geneva)\, Various types of spectra and spectral measures on Schreier and Cayley graphs16.15-17.00 Urs Lang (ETH Zurich)\, Characterizations and asymptotic geometry of rank-n-hyperbolic spaces
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-8/
LOCATION:Salle W (DMA ENS)
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
END:VCALENDAR