BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Département de mathématiques et applications
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:20210328T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20211031T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20210423T150000
DTEND;TZID=Europe/Paris:20210423T162000
DTSTAMP:20260407T091042
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:20210423T163000
DTEND;TZID=Europe/Paris:20210423T175000
DTSTAMP:20260407T091042
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
END:VCALENDAR