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X-WR-CALNAME:Center for Complex Geometry
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220125T150000
DTEND;TZID=Asia/Seoul:20220125T160000
DTSTAMP:20260615T094643
CREATED:20220125T060000Z
LAST-MODIFIED:20220107T014952Z
UID:979-1643122800-1643126400@ccg.ibs.re.kr
SUMMARY:Sanghoon Baek\, Relationship between the Chow and Grothendieck Rings for Generic Flag Varieties
DESCRIPTION:     Speaker\n\n\nSanghoon Baek\nKAIST\n\n\n\n\n\nConsider the canonical morphism from the Chow ring of a smooth variety X to the associated graded ring of the coniveau filtration on the Grothendieck ring of X. In general\, this morphism is not injective. However\, Nikita Karpenko conjectured that these two rings are isomorphic for a generic flag variety X of a semisimple group G\, where he confirmed the conjecture for a simple group G of type A or C. Recently\, this conjecture was disproved by Nobuaki Yagita for some spin groups G. We will discuss further counter-examples using the K-theoretical Pieri formula for highest orthogonal grassmannians. This is joint work with Nikita Karpenko.
URL:https://ccg.ibs.re.kr/event/2022-01-25-1500/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
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DTSTART;TZID=Asia/Seoul:20220125T162000
DTEND;TZID=Asia/Seoul:20220125T172000
DTSTAMP:20260615T094643
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
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