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X-WR-CALNAME:Département de mathématiques et applications
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TZID:Europe/Paris
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DTSTART:20170326T010000
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DTSTART:20171029T010000
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DTSTART;TZID=Europe/Paris:20170310T110000
DTEND;TZID=Europe/Paris:20170310T110000
DTSTAMP:20260412T010904
CREATED:20170310T100000Z
LAST-MODIFIED:20211104T103601Z
UID:8361-1489143600-1489143600@www.math.ens.psl.eu
SUMMARY:Rational points on families of curves
DESCRIPTION:The TAC (torsion anomalous conjecture) states that for an irreducible variety V embedded transversaly in an abelian variety A there are only finitely many maximal V-torsion anomalous varieties. It is well know that the TAC implies the Mordell-Lang conjecture. S. Checcole\, F. Veneziano and myself were trying to prove some new cases of the TAC. In this process we realised that some methods could be made not only effective but even explicit. So we analysed the implication of this explicit methods on the Mordell Conjeture. Namely: can we make the Mordell Conjecture explicit for some new families of curves and so determine all the rational points on these curves? Of course we started with the easiest situation\, that is curves in ExE for E an elliptic curve. We eventually could give some new families of curves of growing genus for which we can determine all the rational points. I will explain the difficulties and the ingredients of this result. I will then discuss the generalisations of the method and also its limits.
URL:https://www.math.ens.psl.eu/evenement/rational-points-on-families-of-curves/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170310T141500
DTEND;TZID=Europe/Paris:20170310T141500
DTSTAMP:20260412T010904
CREATED:20170310T131500Z
LAST-MODIFIED:20211104T104001Z
UID:8367-1489155300-1489155300@www.math.ens.psl.eu
SUMMARY:Quasianalytic Ilyashenko algebras
DESCRIPTION:In 1923\, Dulac published a proof of the claim that every real analytic vector field on the plane has only finitely many limit cycles (now known as Dulac’s Problem). In the mid-1990s\, Ilyashenko completed Dulac’s proof
URL:https://www.math.ens.psl.eu/evenement/quasianalytic-ilyashenko-algebras/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170310T160000
DTEND;TZID=Europe/Paris:20170310T160000
DTSTAMP:20260412T010904
CREATED:20170310T150000Z
LAST-MODIFIED:20211104T104002Z
UID:8368-1489161600-1489161600@www.math.ens.psl.eu
SUMMARY:Satellites of spherical subgroups and Poincaré polynomials
DESCRIPTION:Let G be a connected reductive group over C. One can associate with every spherical homogeneous space G/H its lattice of weights X^*(G/H) and a subset S of M of linearly independent primitive lattice vectors which are called the spherical roots. For any subset I of S we define\, up to conjugation\, a spherical subgroup H_I in G such that dim H_I = dim H and X^*(G/H_I) = X^*(G/H). We call the subgroups H_I the satellites of the spherical subgroup H. Our interest in satellites H_I is motivated by the space of arcs of the spherical homogeneous space G/H.We show a close relation between the Poincaré polynomials of the two spherical homogeneous spaces G/H and G/H_I.All of this is useful for the computation of the stringy E-function of Q-Gorenstein spherical embeddings.The talk is based on joint works with Victor Batyrev.
URL:https://www.math.ens.psl.eu/evenement/satellites-of-spherical-subgroups-and-poincare-polynomials/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
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