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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
TZOFFSETTO:+0900
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DTSTART:20190101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201202T160000
DTEND;TZID=Asia/Seoul:20201202T170000
DTSTAMP:20260616T220204
CREATED:20201126T061653Z
LAST-MODIFIED:20210430T042100Z
UID:240-1606924800-1606928400@ccg.ibs.re.kr
SUMMARY:Nguyen Ngoc Cuong\, Hölder Continuous Solutions to Complex Monge-Ampère Equations and its Applications II
DESCRIPTION:     Speaker\n\n\nNguyen Ngoc Cuong\nKAIST\n\n\n\n\n\nThe Monge-Ampère equations provide Kähler-Einstein metrics on projective manifolds with negative or zero first Chern classes thanks to the AubinYau and Yau theorems. However\, most projective manifolds do not have a negative definite or trivial first Chern class. The study of the canonical metric on these manifolds leads to study degenerate Monge-Ampère equations both on the right hand side and on the background form. It turns out that Hölder continuity is the best regularity we can hope for the solution (quasi-plurisubharmonic potential) to the equation. We discuss situations and criterions such that we will have this property and some applications.\n  \nMore precisely\, let X be a compact Kähler manifold of dimension n and ω a Kähler form on X. We consider the complex Monge-Ampère equation (ddcu+ω)n = µ\, where µ is a given positive measure on X of suitable mass and u is an ω-plurisubharmonic function. We show that the equation admits a Hölder continuous solution if and only if the measure µ\, seen as a functional on a complex Sobolev space W∗(X)\, is Hölder continuous. Here\, denote by W1\,2(X) the Sobolev space of real valued functions f on X such that both f and df are of class L2(X). Then\, the complex Sobolev space W∗(X)\, introduced by Dinh-Sibony\, is the space of all functions f ∈ W1\,2(X) such that\ndf ∧ dcf ≤ T\nfor some closed positive (1\, 1)-current T on X.\n  \nA similar result is also obtained for the complex Monge-Ampère equations on domains of Cn.\n  \nIn the first talk we give motivations and background to study weak solutions of Monge-Ampère equations.\n  \nIn the second talk we focus on the several criterions such that the solution is Hölder continuous\, or alternatively we give the estimate of Hölder norm that depends very weak on the datum such as Lp-norm\, p > 1\, of the right hand sides.\n  \nThis is based on joint work with Tien-Cuong Dinh and Slawomir Ko lodziej.
URL:https://ccg.ibs.re.kr/event/2020-12-02/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201209T160000
DTEND;TZID=Asia/Seoul:20201209T170000
DTSTAMP:20260616T220204
CREATED:20201203T031913Z
LAST-MODIFIED:20210430T042044Z
UID:256-1607529600-1607533200@ccg.ibs.re.kr
SUMMARY:Jihun Yum\, Isometric Embedding of Kähler Manifolds and the Diastatic Function
DESCRIPTION:     Speaker\n\n\nJihun Yum\nIBS\, Center for Complex Geometry
URL:https://ccg.ibs.re.kr/event/2020-12-09/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201210T110000
DTEND;TZID=Asia/Seoul:20201210T120000
DTSTAMP:20260616T220204
CREATED:20201203T100951Z
LAST-MODIFIED:20210430T042026Z
UID:262-1607598000-1607601600@ccg.ibs.re.kr
SUMMARY:Minseong Kwon\, Integrability of G-structures III
DESCRIPTION:     Speaker\n\n\nMinseong Kwon\nKAIST\n\n\n\n\n\n\nThis is a working seminar to introduce the notion of an integrable G-structure and its obstruction class. In the previous two talks\, we discussed the definition of the k-th order structure tensor of a G-structure. In the third talk\, we will discuss how the structure tensors can be characterized in terms of classical invariants\, namely the curvature tensor and the torsion tensor of a given connection. The main reference is the paper ‘The Integrability Problem for G-structures’ (1965) written by Victor Guillemin.
URL:https://ccg.ibs.re.kr/event/2020-12-10/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20201216T160000
DTEND;TZID=Asia/Seoul:20201216T170000
DTSTAMP:20260616T220204
CREATED:20201210T060418Z
LAST-MODIFIED:20210430T042010Z
UID:270-1608134400-1608138000@ccg.ibs.re.kr
SUMMARY:Sung Yeon Kim\, Nonsolvability of Lewy Operator and Non-realizable CR Structures
DESCRIPTION:     Speaker\n\n\nSung Yeon Kim\nIBS\, Center for Complex Geometry
URL:https://ccg.ibs.re.kr/event/2020-12-16/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
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