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DTSTART;TZID=Europe/Paris:20200602T110000
DTEND;TZID=Europe/Paris:20200602T120000
DTSTAMP:20260408T212242
CREATED:20200601T094418Z
LAST-MODIFIED:20200901T073027Z
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SUMMARY:AG - séminaire dématérialisé : Rostislav Devyatov (University of Ottawa) : Multiplicity-free products of Schubert divisors and an application to canonical dimension of torsors
DESCRIPTION:In the first part of my talk I am going to speak about Schubert calculus. Let G/B be a flag variety\, where G is a linear simple algebraic group\, and B is a Borel subgroup. Schubert calculus studies (in classical terms) multiplication in the cohomology ring of a flag variety over the complex numbers\, or (in more algebraic terms) the Chow ring of the flag variety. This ring is generated as a group by the classes of so-called Schubert varieties (or their Poincare duals\, if we speak about the classical cohomology ring)\, i. e. of the varieties of the form BwB/B\, where w is an element of the Weyl group. As a ring\, it is almost generated by the classes of Schubert varieties of codimension 1\, called Schubert divisors. More precisely\, the subring generated by Schubert divisors is a subgroup of finite index. These two facts lead to the following general question: how to decompose a product of Schubert divisors into a linear combination of Schubert varieties. In my talk\, I am going to address (and answer if I have time) two more particular versions of this question: If G is of type A\, D\, or E\, when does a coefficient in such a linear combination equal 0? When does it equal 1? \nIn the second part of my talk I am going to say how to apply these results to theory of torsors and their canonical dimensions. A torsor of an algebraic group G (over an arbitrary field\, here this is important) is a scheme E with an action of G such that over a certain extension of the base field E becomes isomorphic to G\, and the action becomes the action by left shifts of G on itself. The canonical dimension of a scheme X understood as a scheme is the minimal dimension of a subscheme Y of X such that there exists a rational map from X to Y. And the canonical dimension of an algebraic group G understood as a group is the maximum over all field extensions L of the base field of G of the canonical dimensions of all G_L-torsors. In my talk I am going to explain how to get estimates on canonical dimension of certain groups understood as groups using the result from the first part. \n  \nSlides de l’exposé. \nRostislav Devyatov (Page professionnelle ) \n  \n\nL’exposé sera retransmis via BBB (BigBlueButton). \nNom de réunion : « Sem AG 02-06-2020 : Rostislav Devyatov » ; contacter Luc Pirio pour le mot de passe.
URL:https://lmv.math.cnrs.fr/evenenement/ag-seminaire-dematerialise-rostislav-devyatov-university-of-ottawa-multiplicity-free-products-of-schubert-divisors-and-an-application-to-canonical-dimension-of-torsors/
CATEGORIES:Séminaire AG
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200609T130000
DTEND;TZID=Europe/Paris:20200609T140000
DTSTAMP:20260408T212242
CREATED:20200605T153119Z
LAST-MODIFIED:20200622T071719Z
UID:8091-1591707600-1591711200@lmv.math.cnrs.fr
SUMMARY:AG - séminaire dématérialisé : Carolina Araujo  (IMPA - Brazil) : Special subgroups of the Cremona group via Calabi-Yau pairs
DESCRIPTION:The Cremona group in dimension n is the subgroup of birational transformation of the projective space IP^n. Describing the structure of the Cremona group is a major problem in algebraic geometry. While the theory is well developed in dimension 2\, little is known in dimension ≥3. A natural problem is to construct special subgroups of the Cremona group. In 2013\, Blanc described the subgroup of the Cremona group of the plane that preserves the meromorphic volume form ω= (dx/x) ∧ (dy/y). The form ω has simple poles exactly along the 3 coordinate lines. The pair (IP^2\, ω) is an example of a Calabi-Yau pair: a pair (X\,D) where X is a complex projective variety\, and D is the divisor associated to a meromorphic volume form on X. Calabi-Yau pairs appear naturally in the context of the Minimal Model Program\, and have been much investigated. \nIn this talk\, I will explain how one can explore the birational geometry of Calabi-Yau pairs to construct interesting subgroups of the Cremona group in dimension ≥3. \nThis is joint work with Alessio Corti (London\, UK) and Alex Massarenti (Ferrara\, Italy). \n  \nSlides de l’exposé. \n  \n\nL’exposé sera retransmis via Zoom. \nNom de réunion : « Sem AG du LMV – Carolina Araujo » ; contacter Luc Pirio pour le mot de passe.
URL:https://lmv.math.cnrs.fr/evenenement/ag-seminaire-dematerialise-carolina-araujo-impa-brazil-special-subgroups-of-the-cremona-group-via-calabi-yau-pairs/
CATEGORIES:Séminaire AG
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20200623T110000
DTEND;TZID=Europe/Paris:20200623T120000
DTSTAMP:20260408T212242
CREATED:20200622T071856Z
LAST-MODIFIED:20200901T073059Z
UID:8099-1592910000-1592913600@lmv.math.cnrs.fr
SUMMARY:AG - séminaire dématérialisé : Paul Broussous ( Univ. Poitiers ) : Coefficients et vecteurs test explicites
DESCRIPTION:Soit F un corps p-adique. Pour les représentations de la série principale non ramifiée d’un groupe réductif sur F\, on a la notion à présent très classique de fonction sphérique (« zonal spherical function »). Nous étendons cette notion au cas de la série discrète de GL(n\,F). Pour certaines représentations de cette série (dites de « niveau 0 »)\, nous construisons une fonction sphérique explicite. Nous en déduisons des coefficients matriciels explicites. Nous donnons des applications à l’espace symétrique GL(n\,F)/GL(n\,F_0)\, où F/F_0 est une extension quadratique. \nSlides de l’exposé. \n\nL’exposé sera retransmis via Zoom. \nNom de réunion : « Sem AG du LMV – Paul Broussous » ; contacter Luc Pirio pour le mot de passe.
URL:https://lmv.math.cnrs.fr/evenenement/ag-seminaire-dematerialise-paul-broussous-univ-poitiers-coefficients-et-vecteurs-test-explicites/
CATEGORIES:Séminaire AG
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