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X-ORIGINAL-URL:https://ccg.ibs.re.kr
X-WR-CALDESC:Events for Center for Complex Geometry
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20220101T000000
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DTSTART;TZID=Asia/Seoul:20230725T110000
DTEND;TZID=Asia/Seoul:20230725T120000
DTSTAMP:20260510T042210
CREATED:20230712T131020Z
LAST-MODIFIED:20230716T052748Z
UID:2356-1690282800-1690286400@ccg.ibs.re.kr
SUMMARY:Patrick Brosnan\, How Markman Saves the Hodge Conjecture (for Weil Type Abelian Fourfolds) from Kontsevich\, II
DESCRIPTION:    Speaker\n\n\nPatrick Brosnan\nUniversity of Maryland\n\n\n\n\n\n\nI’ll explain what I know about two very interesting pieces of work: \n(1) Markman’s proof of the Hodge conjecture for Weil type abelian fourfolds of discriminant 1. \n(2) Kontsevich’s tropical approach to looking for counterexamples to the Hodge conjecture for Weil type abelian varieties. \nThen I’ll explain a simple observation of mine\, which implies that Kontsevich’s approach cannot work for abelian fourfolds of any discriminant. \nI’ll start out by explaining the statement of (1) precisely along with the geometric input that is required in (2). Then I’ll formulate my observation\, which is really about why the discriminant determines what types of degenerations an abelian fourfold of Weil type can have. Along the way\, I’ll take the opportunity to say a little bit about Markman’s proof of (1).
URL:https://ccg.ibs.re.kr/event/2023-07-25-1100-1200/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
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