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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
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20190331T010000
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TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20191027T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20190111T110000
DTEND;TZID=Europe/Paris:20190111T123000
DTSTAMP:20260409T131433
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:20260409T131433
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:20260409T131433
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
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