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X-WR-CALNAME:Center for Complex Geometry
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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:20250101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260227T163000
DTEND;TZID=Asia/Seoul:20260227T173000
DTSTAMP:20260417T222911
CREATED:20260219T172106Z
LAST-MODIFIED:20260220T064048Z
UID:4441-1772209800-1772213400@ccg.ibs.re.kr
SUMMARY:On the virtual cohomological dimensions of automorphism groups of K3 surfaces
DESCRIPTION:    Speaker\n\n\nTaiki Takatsu\nTokyo University of Science\n\n\n\n\n\n\nWe will discuss Mukai’s conjecture that the virtual cohomological dimension of the automorphism group of a K3 surface is equal to the maximum rank of its Mordell-Weil groups. The action of the automorphism group on the second cohomology induces a natural action on a hyperbolic space. In this talk\, we will explain that Mukai’s conjecture can be regarded as a problem in hyperbolic geometry and geometric group theory via this action. In particular\, we give the formula that determines the virtual cohomological dimension of the automorphism group of a K3 surface by the covering dimension of the blown-up boundary associated with the ample cone of the K3 surface. If time permits\, we will give an affirmative example and a counterexample of Mukai’s conjecture.
URL:https://ccg.ibs.re.kr/event/tba-2/
LOCATION:B236\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
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