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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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TZID:Europe/Paris
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TZOFFSETFROM:+0100
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DTSTART:20190331T010000
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TZOFFSETFROM:+0200
TZOFFSETTO:+0100
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DTSTART:20191027T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190110T160000
DTEND;TZID=Europe/Paris:20190110T173000
DTSTAMP:20260409T132051
CREATED:20190110T150000Z
LAST-MODIFIED:20211104T112500Z
UID:14063-1547136000-1547141400@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-2/
CATEGORIES:Théorie des Modèles et Groupes
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190111T110000
DTEND;TZID=Europe/Paris:20190111T123000
DTSTAMP:20260409T132051
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:20190111T141500
DTEND;TZID=Europe/Paris:20190111T154500
DTSTAMP:20260409T132051
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:20190111T160000
DTEND;TZID=Europe/Paris:20190111T173000
DTSTAMP:20260409T132051
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:20190115T160000
DTEND;TZID=Europe/Paris:20190115T173000
DTSTAMP:20260409T132051
CREATED:20190115T150000Z
LAST-MODIFIED:20211104T111400Z
UID:8481-1547568000-1547573400@www.math.ens.psl.eu
SUMMARY:Density of the union of Cartan subgroups of  o-minimal groups
DESCRIPTION:Let G be a group. A subgroup H of G is a Cartan subgroup  ofG if H is a maximal nilpotent subgroup of G\, and for every normal finiteindex subgroup X of H\, X has finite index in its normalizer in G. \nWe consider Cartan subgroups of  definably connect groups definable inan o-minimal structure. In [BJ0] we proved that\, in this context\,Cartan subgroups of G exist\, they are definable and they fall infinitely many conjugacy classes. \nIn this talk I will prove that the union of the Cartan subgroups isdense in the group\, which was the main question left open in [BBO].(Joint work with Elías Baro and Alessandro Berarducci.) \n [BJ0] E.Baro\, E. Jaligot and M.Otero. Cartan subgroups of groupsdefinable in o-minimal structures\, J. Inst. Math. Juissieu 13 no. 4(2014) 849 – 893.
URL:https://www.math.ens.psl.eu/evenement/density-of-the-union-of-cartan-subgroups-of-o-minimal-groups/
LOCATION:Sophie Germain salle 2015
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190122T140000
DTEND;TZID=Europe/Paris:20190122T170000
DTSTAMP:20260409T132051
CREATED:20190122T130000Z
LAST-MODIFIED:20211104T111601Z
UID:8486-1548165600-1548176400@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie des groupes
DESCRIPTION:Tuesday\, 22 January14.00-14.45 Bertrand Rémy (Ecole Polytechnique)15.00-15.45 Tom Hutchcroft (Cambridge)15.45-16.15 coffee break16.15-17.00 Pavel Zalesski (University of Brasilia)Bertrand Remy\, Quasi-isometric invariance of continuous group Lp-cohomology\, and first applications to vanishings (joint with Marc Bourdon)We show that the continuous L^p-cohomology of locally compact second countable groups is a quasi-isometric invariant. As an application\, we prove partial results supporting a positive answer to a question asked by M. Gromov\, suggesting a classical behaviour of continuous L^p-cohomology of simple real Lie groups. In addition to quasi-isometric invariance\, the ingredients are a spectral sequence argument and Pansu?RTMs vanishing results for real hyperbolic spaces. In the best adapted cases of simple Lie groups\, we obtain nearly half of the relevant vanishings. Tom Hutchcroft\, Kazhdan groups have cost 1I will sketch a proof that Kazhdan groups have cost 1\, answering a question of Gaboriau. No knowledge of Kazhdan groups or of cost will be assumed. Joint work with Gabor Pete.Pavel Zalesski\, The profinite completion of 3-manifold groups.Abstract. We shall present structural results of the profinite completion widehat G of a 3-manifold group G and its interrelation with the structure of G. We shall address the question to what extent the profinite completion of the fundamental group $pi_1M of a 3-manifold determines the manifold M and discuss residual properties of pi_1 M.
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-des-groupes-3/
LOCATION:Salle W ENS
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190129T160000
DTEND;TZID=Europe/Paris:20190129T173000
DTSTAMP:20260409T132051
CREATED:20190129T150000Z
LAST-MODIFIED:20211104T111800Z
UID:8488-1548777600-1548783000@www.math.ens.psl.eu
SUMMARY:Spectrum of the profinite completion of the integers
DESCRIPTION:Using ultraproducts\, I will describe the spectrum of the profinite completion of the integers and of the finite adeles over the rationals.The final aim is to describe the structure sheaf of these structures.Joint work with Margarita Otero and Angus Macintyre.
URL:https://www.math.ens.psl.eu/evenement/spectrum-of-the-profinite-completion-of-the-integers/
LOCATION:Sophie Germain salle 1016
CATEGORIES:Théorie des Modèles et Groupes
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