BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
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:20220327T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20221030T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20221125T110000
DTEND;TZID=Europe/Paris:20221125T123000
DTSTAMP:20260427T045836
CREATED:20221122T152309Z
LAST-MODIFIED:20221122T152714Z
UID:16121-1669374000-1669379400@www.math.ens.psl.eu
SUMMARY:Taming perfectoid fields
DESCRIPTION:Tilting perfectoid fields\, developed by Scholze\, allows to transfer results between certain henselian fields of mixed characteristic and their positive characteristic counterparts and vice versa. We present a model-theoretic approach to tilting via ultraproducts\, which allows to transfer many first-order properties between a perfectoid field and its tilt (and conversely). In particular\, our method yields a simple proof of the Fontaine-Wintenberger Theorem which states that the absolute Galois group of a perfectoid field and its tilt are canonically isomorphic. A key ingredient in our approach is an Ax-Kochen/Ershov principle for perfectoid fields (and generalizations thereof).\nThis is joint work with Konstantinos Kartas.
URL:https://www.math.ens.psl.eu/evenement/taming-perfectoid-fields/
LOCATION:IHP salle 01
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20221125T141500
DTEND;TZID=Europe/Paris:20221125T154500
DTSTAMP:20260427T045836
CREATED:20221122T152504Z
LAST-MODIFIED:20221122T152638Z
UID:16123-1669385700-1669391100@www.math.ens.psl.eu
SUMMARY:Abundance of strongly minimal autonomous differential equations
DESCRIPTION:In several classical families of differential equations such as the Painlevé families (Nagloo\, Pillay) or finite dimensional families of Schwarzian differential equations (Blazquez-Sanz\, Casale\, Freitag\, Nagloo)\, the following picture has been obtained regarding the transcendence properties of their solutions: \n– (Strong minimality): outside of an exceptional set of parameters\, the corresponding differential equations are strongly minimal\,\n– (Geometric triviality): algebraic independence of several solutions is controlled by pairwise algebraic independence outside of this exceptional set of parameters\,\n– (Multidimensionality): the differential equations defined by generic independent parameters are orthogonal. \nAre the families of differential equations satisfying such transcendence properties scarce or abundant in the universe of algebraic differential equations? \nI will describe an abundance result for families of autonomous differential equations satisfying the first two properties. The model-theoretic side of the proof uses a fine understanding of the structure of autonomous differential equations internal to the constants that we have recently obtained in a joint work with Rahim Moosa. The geometric side of the proof uses a series of papers of S.C. Coutinho and J.V. Pereira on the dynamical properties of a generic foliation.
URL:https://www.math.ens.psl.eu/evenement/abundance-of-strongly-minimal-autonomous-differential-equations/
LOCATION:IHP salle 01
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20221125T160000
DTEND;TZID=Europe/Paris:20221125T173000
DTSTAMP:20260427T045836
CREATED:20221122T152916Z
LAST-MODIFIED:20221122T152916Z
UID:16127-1669392000-1669397400@www.math.ens.psl.eu
SUMMARY:On non-Diophantine sets in rings of functions
DESCRIPTION:For a ring R\, a subset of a cartesian power of R is said to be Diophantine if it is positive existentially definable over R with parameters from R. In general\, Diophantine sets over rings are not well-understood even in very natural situations; for instance\, we do not know if the ring of integers Z is Diophantine in the field of rational numbers. To show that a set is Diophantine requires to produce a particular existential formula that defines it. However\, to show that a set is not Diophantine is a more subtle task; in lack of a good description of Diophantine sets it requires to find at least a property shared by all of them. I will give an outline of some recent joint work with Garcia-Fritz and Pheidas on showing that several sets and relations over rings of polynomials and rational functions that are not Diophantine.
URL:https://www.math.ens.psl.eu/evenement/on-non-diophantine-sets-in-rings-of-functions/
LOCATION:IHP salle 01 et zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
END:VCALENDAR