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X-WR-CALDESC:Events for Center for Complex Geometry
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DTSTART:20240101T000000
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BEGIN:VEVENT
DTSTART;VALUE=DATE:20250301
DTEND;VALUE=DATE:20260216
DTSTAMP:20260415T172300
CREATED:20250304T080834Z
LAST-MODIFIED:20250304T081528Z
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SUMMARY:Ngoc Cuong Nguyen (KAIST)
DESCRIPTION:Ngoc Cuong Nguyen\nVisitor (2025.3.1-2026.2.15) from KAIST\nOffice: B248
URL:https://ccg.ibs.re.kr/event/250301-260215/
CATEGORIES:Visitors
ATTACH;FMTTYPE=image/jpeg:https://ccg.ibs.re.kr/wp-content/uploads/2025/03/ncnguyen_rescaled-1.jpg
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260226T160000
DTEND;TZID=Asia/Seoul:20260226T170000
DTSTAMP:20260415T172300
CREATED:20260219T171800Z
LAST-MODIFIED:20260219T171938Z
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SUMMARY:On Slope Unstable Fano varieties
DESCRIPTION:    Speaker\n\n\nYen-An Chen\nKIAS\n\n\n\n\n\n\nFor Fano varieties\, significant progress has been made recently in the study of K-stability\, while the understanding of the weaker but more algebraic concept of $(−K)$-slope stability remains intricate. For instance\, a conjecture attributed to Iskovskikh states that the tangent bundle of a Picard rank one Fano manifold is slope stable. Peternell-Wisniewski and Hwang proved this conjecture up to dimension five in 1998\, but Kanemitsu later disproved it in 2021. To address this gap in understanding\, we present a method that aims to characterize the geometry associated with the maximal destabilizing sheaf of the tangent sheaf of a Fano variety. This approach utilizes modern advancements in the foliated minimal model program. In dimension two\, our approach leads to a complete classification of $(−K)$-slope unstable weak del Pezzo surfaces with canonical singularities. As by-products\, we provide the first conceptual proof that $\mathbb{P}^1 \times \mathbb{P}^1$ and $\mathbb{F}_1$ are the only $(−K)$-slope unstable nonsingular del Pezzo surfaces\, recovering a classical result of Fahlaoui in 1989. This is the joint work with Ching-Jui Lai.
URL:https://ccg.ibs.re.kr/event/on-slope-unstable-fano-varieties/
LOCATION:B236\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260227T163000
DTEND;TZID=Asia/Seoul:20260227T173000
DTSTAMP:20260415T172300
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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