BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Center for Complex Geometry - ECPv6.15.20//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-ORIGINAL-URL:https://ccg.ibs.re.kr
X-WR-CALDESC:Events for Center for Complex Geometry
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20210101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220125T162000
DTEND;TZID=Asia/Seoul:20220125T172000
DTSTAMP:20260512T122228
CREATED:20220125T072000Z
LAST-MODIFIED:20220112T014905Z
UID:981-1643127600-1643131200@ccg.ibs.re.kr
SUMMARY:Rostislav Devyatov\, Multiplicity-free Products of Schubert Divisors and an Application to Canonical Dimension
DESCRIPTION:     Speaker\n\n\nRostislav Devyatov\nKAIST\n\n\n\n\n\n\nIn 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 will define canonical dimension of varieties (which\, roughly speaking\, measures how hard it is to get a rational point in a given variety) and canonical dimension of algebraic groups (which\, roughly speaking\, measures how complicated the torsors of an algebraic group can be). Then I will state a theorem about an upper estimate on the canonical dimension of the group and its torsors following from the fact that a certain coefficient we obtained in the first part of my talk (i. e. the coefficient in the decomposition of a product of Schubert divisors into a linear combination of Schubert varieties) equals 1. As a result\, we will get some explicit numerical estimates on canonical dimension of simply connected simple split algebraic groups of type A\, D\, and E.
URL:https://ccg.ibs.re.kr/event/2022-01-25-1620/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
END:VCALENDAR