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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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DTSTART:20190331T010000
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DTSTART:20191027T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191001T160000
DTEND;TZID=Europe/Paris:20191001T173000
DTSTAMP:20260424T173312
CREATED:20191001T140000Z
LAST-MODIFIED:20211025T103654Z
UID:8515-1569945600-1569951000@www.math.ens.psl.eu
SUMMARY:Sous-groupes qui pavent génériquement et géométrie des involutions
DESCRIPTION:(En collaboration avec Joshua Wiscons)L’exposé mélange théorie des modèles\, théorie des groupes\, et algèbre géométrique. On y parlera de groupes de rang de Morley fini\, mais il suffit de savoir naïvement ce qu’est une dimension à valeurs entières\, sans devoir maîtriser les finesses de la conjecture de Cherlin-Zilber.Un groupe abstrait porte peu d’information de nature géométrique\, même au sens des géométries d’incidence\, et c’est toujours remarquable si cela se produit.Le pur groupe SO(3\,R)\, par exemple\, permet de redéfinir l’espace projectif réel. PGL(2\,C) permet presque la même chose : il définit un fragment générique de l’espace projectif complexe. En fait cette situation est naturellement liée à la distribution des involutions et aux intersections entre conjugués de leur centralisateur\, qui pavent génériquement le groupe ambiant (tout cela sera expliqué dans SO(3\,R) et PGL(2\,C)).En suivant cette piste on peut obtenir des énoncés étonnamment forts\, généralisant au passage divers classiques sur les mauvais groupes ou sur les groupes définissablement linéaires de rang de Morley fini. On conjecture également que cette géométrie des involutions annonce un nouveau théorème d’identification pour PGL(2\, K).
URL:https://www.math.ens.psl.eu/evenement/sous-groupes-qui-pavent-generiquement-et-geometrie-des-involutions/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191008T160000
DTEND;TZID=Europe/Paris:20191008T173000
DTSTAMP:20260424T173312
CREATED:20191008T140000Z
LAST-MODIFIED:20211104T140837Z
UID:8522-1570550400-1570555800@www.math.ens.psl.eu
SUMMARY:An abstract elementary class framework for fields with commuting automorphisms
DESCRIPTION:We take a look at structures that consist of a field together with finitely many distinguished field automorphisms required to commute. The theory of fields with one distinguished automorphism has a model companion known as ACFA\, which Z. Chatzidakis and E. Hrushovski have studied in depth. However\, Hrushovski has proved that if you look at fields with two or more commuting automorphisms\, then the existentially closed models of the theory do not form a first order model class. This leads us to investigate them within a non-elementary framework. One way of doing non-elementary model theory is to move from elementary classes to the more general setting of abstract elementary classes (AECs). In the first order world\, classes of structures are usually defined syntactically as model classes of a given first order theory. An AEC is defined more semantically\, as a class of structures together with a binary relation that generalises the first-order elementary submodel relation. In this talk\, we go through some basics of AECs and present an AEC framework for studying fields with commuting automorphisms.
URL:https://www.math.ens.psl.eu/evenement/an-abstract-elementary-class-framework-for-fields-with-commuting-automorphisms/
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191022T160000
DTEND;TZID=Europe/Paris:20191022T173000
DTSTAMP:20260424T173312
CREATED:20191022T140000Z
LAST-MODIFIED:20211025T103725Z
UID:8526-1571760000-1571765400@www.math.ens.psl.eu
SUMMARY:The transitivity of Kim-independence
DESCRIPTION:The class of NSOP_1 theories contains the simple theories and many interesting non-simple theories\, such as the omega-free PAC fields or generic vector spaces with a non-degenerate bilinear form. With Itay Kaplan\, we introduced Kim-independence which agrees with non-forking independence within the simple theories and shares many of its nice properties within the simple NSOP_1 context. One very basic roadblock in lifting simplicity theory to the NSOP_1 setting\, however\, was transitivity: a free extension of a free extension should still be a free extension. This is almost immediate for non-forking extensions in a simple theory\, but becomes more involved for free extensions in the sense of Kim-independence. We will describe and motivate the basic theory\, and then discuss our recent proof of transitivity. This is joint with Itay Kaplan.
URL:https://www.math.ens.psl.eu/evenement/the-transitivity-of-kim-independence/
LOCATION:Sophie Germain salle 1016
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20191029T160000
DTEND;TZID=Europe/Paris:20191029T173000
DTSTAMP:20260424T173312
CREATED:20191029T150000Z
LAST-MODIFIED:20211104T140810Z
UID:8529-1572364800-1572370200@www.math.ens.psl.eu
SUMMARY:Model theory of proalgebraic groups
DESCRIPTION:Inspired by the model theoretic study of profinite groups\, we discuss the foundations of a model theoretic approach to proalgebraic groups. Our axiomatization is based on the tannakian philosophy. Through a tensor analog of skeletal categories we are able to consider neutral tannakian categories with a fibre functor as many-sorted first order structures. The theory of a diagonalizable proalgebraic group is well understood. It is determined by the theory of the base field and the theory of its character group. This is joint work with Anand Pillay.
URL:https://www.math.ens.psl.eu/evenement/model-theory-of-proalgebraic-groups/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
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