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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
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TZID:Europe/Paris
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TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20160327T010000
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DTSTART:20161030T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20160513T110000
DTEND;TZID=Europe/Paris:20160513T110000
DTSTAMP:20260415T062201
CREATED:20160513T090000Z
LAST-MODIFIED:20211104T100810Z
UID:8279-1463137200-1463137200@www.math.ens.psl.eu
SUMMARY:Non-standard fewnomials
DESCRIPTION:Call non-standard fewnomial (or sparse/lacunary polynomial) a non-standard polynomial whose number of non-zero terms is finite. The non-standard translation of a conjecture of Rényi and Erdöt
URL:https://www.math.ens.psl.eu/evenement/non-standard-fewnomials/
LOCATION:Salle W ENS
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20160513T141500
DTEND;TZID=Europe/Paris:20160513T141500
DTSTAMP:20260415T062201
CREATED:20160513T121500Z
LAST-MODIFIED:20211104T100811Z
UID:8280-1463148900-1463148900@www.math.ens.psl.eu
SUMMARY:Profinite NIP groups
DESCRIPTION:We consider profinite groups as 2-sorted first order structures\, with a group sort\, and a second sort which acts as an index set for a uniformly definable basis of neighbourhoods of the identity. It is shown that if the basis consists of all open subgroups\, then the first order theory of such a structure is NIP (that is\, does not have the independence property) precisely if the group has a normal subgroup of finite index which is a direct product of finitely many compact p-adic analytic groups\, for distinct primes p. In fact\, the condition NIP can here be weakened to NTP2.We also show that any NIP profinite group\, presented as a 2-sorted structure\, has an open prosoluble normal subgroup.(Joint work with Dugald Macpherson)
URL:https://www.math.ens.psl.eu/evenement/profinite-nip-groups/
LOCATION:Salle W ENS
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20160513T160000
DTEND;TZID=Europe/Paris:20160513T160000
DTSTAMP:20260415T062201
CREATED:20160513T140000Z
LAST-MODIFIED:20211104T100811Z
UID:8281-1463155200-1463155200@www.math.ens.psl.eu
SUMMARY:Wave front sets of distributions in non-archimedean analysis
DESCRIPTION:In 1969\, Sato and Hörmander introduced the notion of wave front set of a distribution in the real context. This concept gives a better understanding of operations on distributions such as product or pullback and it plays an important role in the theory of partial differential equations. In 1981\, Howe introduced a notion of wave front set for some Lie group representations and in 1985\, Heifetz gave an analogous version in the p-adic context. In this talk\, in the t-adic context in characteristic zero\, using Cluckers-Loeser motivic integration we will present analogous constructions of test functions\, distributions and wave front sets. In particular\, we will explain how definability can be used as a substitute for topological compactness of the sphere in the real and p-adic contexts to obtain finiteness.This a joint work with R. Cluckers\, and F. Loeser.
URL:https://www.math.ens.psl.eu/evenement/wave-front-sets-of-distributions-in-non-archimedean-analysis/
LOCATION:Salle W ENS
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20160520T140000
DTEND;TZID=Europe/Paris:20160520T150000
DTSTAMP:20260415T062201
CREATED:20160520T120000Z
LAST-MODIFIED:20211104T100826Z
UID:8283-1463752800-1463756400@www.math.ens.psl.eu
SUMMARY:Irreducibility of Polynomials over Number Fields is Diophantine
DESCRIPTION:We show that irreducibility of a polynomial in any number of variables over a number field is a diophantine condition\, i.e. captured by an existential formula. This generalises a previous result by Colliot-Thélène and Van Geel that the set of non-nth-powers is diophantine for any n. Our method is heavily based on the Brauer group\, originating from Poonen’s use of quaternion algebras as a technical tool for first-order definitions in number fields.
URL:https://www.math.ens.psl.eu/evenement/irreducibility-of-polynomials-over-number-fields-is-diophantine/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20160520T151500
DTEND;TZID=Europe/Paris:20160520T161500
DTSTAMP:20260415T062201
CREATED:20160520T131500Z
LAST-MODIFIED:20211104T100826Z
UID:8284-1463757300-1463760900@www.math.ens.psl.eu
SUMMARY:The Lang-Vojta conjecture and smooth hypersurfaces over number fields.
DESCRIPTION:Siegel proved the finiteness of the set of solutions to the unit equation in a number ring\, i.e.\, for a number field K with ring of integers O\, the equation x+y=1 has only finitely many solutions in O*. That is\, reformulated in more algebro-geometric terms\, the hyperbolic curve P^1-{0\,1\,infinite} has only finitely many ‘integral points’. In 1983\, Faltings proved the Mordell conjecture generalizing Siegel’s theorem: a hyperbolic complex algebraic curve has only finitely many integral points. Inspired by Faltings’s and Siegel’s finiteness results\, Lang and Vojta formulated a general finiteness conjecture for ‘integral points’ on complex algebraic varieties: a hyperbolic complex algebraic variety has only finitely many ‘integral points’. In this talk we will start by explaining the Lang-Vojta conjecture and then proceed to prove some of its consequences for the arithmetic of homogeneous polynomials over number fields. This is joint work with Daniel Loughran.
URL:https://www.math.ens.psl.eu/evenement/the-lang-vojta-conjecture-and-smooth-hypersurfaces-over-number-fields/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20160520T164500
DTEND;TZID=Europe/Paris:20160520T174500
DTSTAMP:20260415T062201
CREATED:20160520T144500Z
LAST-MODIFIED:20211104T100826Z
UID:8285-1463762700-1463766300@www.math.ens.psl.eu
SUMMARY:La composition de Gauss pour les points entiers primitifs de sphères\, en suivant\, partiellement\, Gunawan.
DESCRIPTION:Gauss a donné des formules pour le nombre de points entiers primitifs de la 2-sphère de rayon au carré égal à n. Ces formules sont en termes de nombres de classes d’anneaux quadratiques de discriminant étroitement liés à n. Cela mène à la question de savoir si ceci peut être expliqué par une action libre et transitive du groupe de Picard de cet anneau sur l’ensemble des tels points entiers primitifs à symétries globales SO_3(Z) près. Ceci est en effet le cas\, et cette action peut être explicitée. L’outil utilisé est la théorie des schémas en groupes sur Z\, ce qui est plus direct que la cohomologie galoisienne et les adèles\, et remarquablement élémentaire. En fait\, Gross et Bhargava demandent une telle approche dans leur article ‘Arithmetic invariant theory’.
URL:https://www.math.ens.psl.eu/evenement/la-composition-de-gauss-pour-les-points-entiers-primitifs-de-spheres-en-suivant-partiellement-gunawan/
LOCATION:ENS Salle W
CATEGORIES:Variétés rationnelles
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