BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Laboratoire de Mathématiques de Versailles - ECPv6.3.5//NONSGML v1.0//EN CALSCALE:GREGORIAN METHOD:PUBLISH X-WR-CALNAME:Laboratoire de Mathématiques de Versailles X-ORIGINAL-URL:https://lmv.math.cnrs.fr X-WR-CALDESC:évènements pour Laboratoire de Mathématiques de Versailles 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:20200329T010000 END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:20201025T010000 END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTART;TZID=Europe/Paris:20200602T110000 DTEND;TZID=Europe/Paris:20200602T120000 DTSTAMP:20240329T164436 CREATED:20200601T094418Z LAST-MODIFIED:20200901T073027Z UID:8086-1591095600-1591099200@lmv.math.cnrs.fr 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. \nAG – séminaire dématérialisé : Rostislav Devyatov (University of Ottawa) : Multiplicity-free products of Schubert divisors and an application to canonical dimension of torsors 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 END:VCALENDAR