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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:20200101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220216T110000
DTEND;TZID=Asia/Seoul:20220216T120000
DTSTAMP:20260417T032259
CREATED:20220216T020000Z
LAST-MODIFIED:20220212T105153Z
UID:987-1645009200-1645012800@ccg.ibs.re.kr
SUMMARY:Chenyang Xu\, K-stability of Fano Varieties
DESCRIPTION:     Speaker\n\n\nChenyang Xu\nPrinceton Univ.\n\n\n\n\n\nK-stability of Fano varieties was initiated as a central topic in complex geometry\, for its relation with the Kähler-Einstein metric. It turns out that the machinery of higher dimensional geometry\, developed around the minimal model program\, provides a fundamental tool to study it\, and therefore makes it an active algebraic subject. This meeting of two well-studied fields has made a number of major conjectures solved. In this talk\, I will survey the recent development.
URL:https://ccg.ibs.re.kr/event/2022-02-16-1100/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220210T110000
DTEND;TZID=Asia/Seoul:20220210T120000
DTSTAMP:20260417T032259
CREATED:20220210T020000Z
LAST-MODIFIED:20220124T121022Z
UID:1027-1644490800-1644494400@ccg.ibs.re.kr
SUMMARY:Young-Hoon Kiem\, A New Construction of the Moduli Space of Pointed Stable Curves of Genus 0
DESCRIPTION:     Speaker\n\n\nYoung-Hoon Kiem\nSeoul National University\n\n\n\n\n\nThe moduli space of n points on a projective line up to projective equivalence has been a topic of research since the 19th century. A natural moduli theoretic compactification was constructed by Deligne and Mumford as an algebraic stack. Later\, Knudsen\, Keel\, Kapranov and others provided explicit constructions by sequences of blowups. The known inductive constructions of Knudsen and Keel however are rather inconvenient when one wants to compute the cohomology of the compactified moduli space as a representation space of its automorphism group because the blowup sequences are not equivariant. I will talk about a new inductive construction of the much studied moduli space from the perspective of sheaf theory. In fact\, we consider the moduli space of rank 1 stable pairs over the moduli space of n pointed stable curves of genus 0. By studing the wall crossing\, we obtain an equivariant sequence of blowups which ends up with the moduli space of n+1 pointed stable curves of genus 0. As an application\, we provide a closed formula of the character of the cohomology of the moduli space. We also provide a partial answer to a question of Manin and Orlov which asks whether the cohomology is a permutation representation or not. Based on a joint work with Jinwon Choi and Donggun Lee.
URL:https://ccg.ibs.re.kr/event/2022-02-10/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220208T110000
DTEND;TZID=Asia/Seoul:20220208T120000
DTSTAMP:20260417T032259
CREATED:20220208T020000Z
LAST-MODIFIED:20220126T010701Z
UID:975-1644318000-1644321600@ccg.ibs.re.kr
SUMMARY:Sandor Kovacs\, Hodge Sheaves for Singular Families
DESCRIPTION:     Speaker\n\n\nSandor Kovacs\nUniv. of Washington\n\n\n\n\n\nThis is a report on joint work with Behrouz Taji. Given a flat projective morphism f : X → B of complex varieties\, assuming that B is smooth\, we construct a functorial system of reflexive Hodge sheaves on B . If in addition\, X is also smooth then this system gives an extension of the Hodge bundle underlying the VHS of the smooth locus of f . This in turn provides a criterion that all VHSs of geometric origin must satisfy. As an independent application we prove a singular version of Viehweg’s conjecture about base spaces of families of maximal variation.
URL:https://ccg.ibs.re.kr/event/2022-02-08/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220127T110000
DTEND;TZID=Asia/Seoul:20220127T120000
DTSTAMP:20260417T032259
CREATED:20220127T020000Z
LAST-MODIFIED:20220103T112105Z
UID:306-1643281200-1643284800@ccg.ibs.re.kr
SUMMARY:Jongbaek Song\, Regular Hessenberg Varieties and Toric Varieties
DESCRIPTION:     Speaker\n\n\nJongbaek Song\nKIAS\n\n\n\n\n\nA Hessenberg variety is a subvariety of the flag variety (G/B) determined by two parameters: one is an element of the Lie algebra of G and the other is a B-submodule containing the Lie algebra of B\, known as a Hessenberg space. In this talk\, we focus on elements in the regular locus of the Lie algebra and the Hessenberg space determined by negative simple roots. Then\, we aim to figure out cohomological relationship of these Hessenberg varieties with a certain class of toric varieties having orbifold singularities. The main result raises an interesting topic concerning toric varieties with symmetries by reflections. This is a joint work with M. Masuda\, T. Horiguchi and J. Shareshian.
URL:https://ccg.ibs.re.kr/event/2022-01-27/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220125T162000
DTEND;TZID=Asia/Seoul:20220125T172000
DTSTAMP:20260417T032259
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
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220125T150000
DTEND;TZID=Asia/Seoul:20220125T160000
DTSTAMP:20260417T032259
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
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220120T110000
DTEND;TZID=Asia/Seoul:20220120T120000
DTSTAMP:20260417T032259
CREATED:20220120T020000Z
LAST-MODIFIED:20211227T043533Z
UID:991-1642676400-1642680000@ccg.ibs.re.kr
SUMMARY:Han-Bom Moon\, Derived Category of Moduli of Vector Bundles II
DESCRIPTION:     Speaker\n\n\nHan-Bom Moon\nFordham University\n\n\n\n\n\nThe derived category of a smooth projective variety is an object expected to encode much birational geometric information. Recently\, there have been many results on decomposing derived categories into simpler building blocks. In the first lecture\, I will provide an elementary introduction to two independent topics — 1. the definition and basic properties of the derived category and 2. moduli spaces of vector bundles on a curve. In the second lecture\, I will present recent progress on the structure of the derived category of the moduli space. Most of the lectures will be accessible to graduate students with basic knowledge of algebraic geometry. The second lecture is based on ongoing joint work with Kyoung-Seog Lee.
URL:https://ccg.ibs.re.kr/event/2022-01-20/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220119T100000
DTEND;TZID=Asia/Seoul:20220119T120000
DTSTAMP:20260417T032259
CREATED:20220119T010000Z
LAST-MODIFIED:20211227T043507Z
UID:910-1642586400-1642593600@ccg.ibs.re.kr
SUMMARY:Han-Bom Moon\, Derived Category of Moduli of Vector Bundles I
DESCRIPTION:     Speaker\n\n\nHan-Bom Moon\nFordham University\n\n\n\n\n\nThe derived category of a smooth projective variety is an object expected to encode much birational geometric information. Recently\, there have been many results on decomposing derived categories into simpler building blocks. In the first lecture\, I will provide an elementary introduction to two independent topics — 1. the definition and basic properties of the derived category and 2. moduli spaces of vector bundles on a curve. In the second lecture\, I will present recent progress on the structure of the derived category of the moduli space. Most of the lectures will be accessible to graduate students with basic knowledge of algebraic geometry. The second lecture is based on ongoing joint work with Kyoung-Seog Lee.
URL:https://ccg.ibs.re.kr/event/2022-01-19/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220118T110000
DTEND;TZID=Asia/Seoul:20220118T120000
DTSTAMP:20260417T032259
CREATED:20220118T020000Z
LAST-MODIFIED:20211213T012913Z
UID:959-1642503600-1642507200@ccg.ibs.re.kr
SUMMARY:Kento Fujita\, The Calabi Problem for Fano Threefolds
DESCRIPTION:     Speaker\n\n\nKento Fujita\nOsaka Univ.\n\n\n\n\n\n\nThere are 105 irreducible families of smooth Fano threefolds\, which have been classified by Iskovskikh\, Mori and Mukai. For each family\, we determine whether its general member admits a Kähler-Einstein metric or not. This is a joint work with Carolina Araujo\, Ana-Maria Castravet\, Ivan Cheltsov\, Anne-Sophie Kaloghiros\, Jesus Martinez-Garcia\, Constantin Shramov\, Hendrik Suess and Nivedita Viswanathan.
URL:https://ccg.ibs.re.kr/event/2022-01-18/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211228T160000
DTEND;TZID=Asia/Seoul:20211228T170000
DTSTAMP:20260417T032259
CREATED:20211228T070000Z
LAST-MODIFIED:20211228T111500Z
UID:919-1640707200-1640710800@ccg.ibs.re.kr
SUMMARY:Paul-Andi Nagy\, Einstein Deformations of Hyperkaehler Cones
DESCRIPTION:     Speaker\n\n\nPaul-Andi Nagy\nIBS CCG\n\n\n\n\n\nFor a hyperkaehler cone with compact link (M\, g) we describe the Einstein deformation theory of g and relate it to the algebraic geometry of the twistor space Z of M. This is joint work with Uwe Semmelmann.
URL:https://ccg.ibs.re.kr/event/2021-12-28-1600/
LOCATION:B236\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211228T110000
DTEND;TZID=Asia/Seoul:20211228T120000
DTSTAMP:20260417T032259
CREATED:20211228T020000Z
LAST-MODIFIED:20211213T012857Z
UID:885-1640689200-1640692800@ccg.ibs.re.kr
SUMMARY:Olivier Martin\, Measures of Association for Algebraic Varieties
DESCRIPTION:     Speaker\n\n\nOlivier Martin\nStony Brook Univ.\n\n\n\n\n\n\nI will discuss recent work in collaboration with R. Lazarsfeld which explores the following question: Given varieties X and Y of the same dimension how far are they from being birational? I will define various “measures of association” which quantify the failure of X and Y to be birational and present partial results\, heuristics\, and several open problems. For instance\, given an n-fold Z dominating very general hypersurfaces X and Y in Pn+1 of degrees d\,e > 2n+1\, we show that the degrees of the projections Z—>X and Z—>Y are at least d and e. Moreover\, given very general hyperelliptic curves X and Y\, any hyperelliptic curve in XxY is contracted by the projection to X or the projection to Y.
URL:https://ccg.ibs.re.kr/event/2021-12-28/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211209T163000
DTEND;TZID=Asia/Seoul:20211209T172000
DTSTAMP:20260417T032259
CREATED:20211209T073000Z
LAST-MODIFIED:20211122T014017Z
UID:829-1639067400-1639070400@ccg.ibs.re.kr
SUMMARY:Yeongrak Kim\, Ulrich Bundles on Cubic Fourfolds
DESCRIPTION:     Speaker\n\n\nYeongrak Kim\nPusan National Univ.\n\n\n\n\n\n\n(This is a part of Algebraic Geometry Day at CCG in IBS.) \nUlrich bundles are geometric objects corresponding to maximally generated maximal Cohen-Macaulay modules\, whose existence has several interesting applications in commutative algebra\, homological algebra\, and linear algebra. After a pioneering work of Beauville and Eisenbud-Schreyer\, existence and classification of Ulrich bundles become important questions also in projective geometry. For instance\, they could help to understand the cone of cohomology tables of coherent sheaves on the underlying projective variety\, determinantal representations of hypersurfaces\, and determinantal representations of Cayley-Chow forms. In this talk\, I will discuss construction of Ulrich bundles on smooth cubic fourfolds. Unlike smooth cubic surfaces or threefolds\, the smallest possible rank of Ulrich bundles on a smooth cubic fourfold may vary if it is special\, i.e.\, X contains certain surfaces which are not homologous to complete intersections. On the other hand\, a (very) general cubic fourfold does not have an Ulrich bundle of rank <6. I will explain how to construct a rank 6 Ulrich bundle on an arbitrary smooth cubic fourfold. This is a joint work with Daniele Faenzi.
URL:https://ccg.ibs.re.kr/event/2021-12-09-1630/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211209T152000
DTEND;TZID=Asia/Seoul:20211209T161000
DTSTAMP:20260417T032259
CREATED:20211209T062000Z
LAST-MODIFIED:20211122T013859Z
UID:826-1639063200-1639066200@ccg.ibs.re.kr
SUMMARY:DongSeon Hwang\, Manin’s Conjecture for a Log Del Pezzo Surface of Index 2
DESCRIPTION:     Speaker\n\n\nDongSeon Hwang\nAjou Univ.\n\n\n\n\n\n\n(This is a part of Algebraic Geometry Day at CCG in IBS.) \nManin’s conjecture predicts the asymptotic behavior on the number of rational points of bounded anticanonical height on Fano varieties. In this talk\, I will explain how the geometry governs the arithmetic in the case of a log del Pezzo surface with A4 and K5 singularities using the torsor method. This talk is based on joint work in progress with Ulrich Derenthal.
URL:https://ccg.ibs.re.kr/event/2021-12-09-1520/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211209T140000
DTEND;TZID=Asia/Seoul:20211209T145000
DTSTAMP:20260417T032259
CREATED:20211209T050000Z
LAST-MODIFIED:20211207T022951Z
UID:824-1639058400-1639061400@ccg.ibs.re.kr
SUMMARY:Kangjin Han\, On the Singular Loci of Higher Secants of Veronese Varieties
DESCRIPTION:     Speaker\n\n\nKangjin Han\nDGIST\n\n\n\n\n\n\n(This is a part of Algebraic Geometry Day at CCG in IBS.) \nFor a projective variety X in PN\, the k-secant variety σk(X) is defined to be the closure of the union of k-planes in PN spanned by k-points of X. In this talk\, we consider singular loci of higher secant varieties of the image of the d-uple Veronese embedding of projective n-space\, νd(Pn). For the singular loci of k-secant of νd(Pn)\, it has been known only for k≤3. First\, I will review some basic notions and results and then explain projective techniques with respect to an explicit calculation of the Gauss map of X and computation for conormal space via a certain type of Young flattening. As investigating geometry of moving tangents along subvarieties\, we determine the (non-)singularity of so-called ‘subsecant loci’ of k-secant of νd(Pn) for arbitrary k. This is a joint work with Katsuhisa Furukawa.
URL:https://ccg.ibs.re.kr/event/2021-12-09-1400/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20211209
DTEND;VALUE=DATE:20211210
DTSTAMP:20260417T032259
CREATED:20211208T150000Z
LAST-MODIFIED:20220124T011541Z
UID:831-1639008000-1639094399@ccg.ibs.re.kr
SUMMARY:Algebraic Geometry Day at CCG in IBS
DESCRIPTION:List of Seminars \n\n\n\n\n\nOn the Singular Loci of Higher Secants of Veronese Varieties\nKangjin Han (DGIST)\n14:00-14:50\, online \n\n\nManin’s Conjecture for a Log Del Pezzo Surface of Index 2\nDongSeon Hwang (Ajou Univ.)\n15:20-16:10\, IBS B266 \n\n\nUlrich Bundles on Cubic Fourfolds\nYeongrak Kim (Pusan National Univ.)\n16:30-17:20\, IBS B266
URL:https://ccg.ibs.re.kr/event/2021-12-09/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Conferences and Workshops
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211202T110000
DTEND;TZID=Asia/Seoul:20211202T120000
DTSTAMP:20260417T032259
CREATED:20211202T020000Z
LAST-MODIFIED:20211123T040520Z
UID:883-1638442800-1638446400@ccg.ibs.re.kr
SUMMARY:Sai-Kee Yeung\, Almost Complex Structures and Complex Structures on Manifolds of Even Dimension at Least 6
DESCRIPTION:     Speaker\n\n\nSai-Kee Yeung\nPurdue University\n\n\n\n\n\nWe would like to explain for each real even dimension 2n ≥ 6 some examples of compact differentiable manifolds supporting an almost complex structure which cannot be deformed to an integrable complex structure.
URL:https://ccg.ibs.re.kr/event/2021-12-02/
LOCATION:on-line
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211123T110000
DTEND;TZID=Asia/Seoul:20211123T120000
DTSTAMP:20260417T032259
CREATED:20211123T020000Z
LAST-MODIFIED:20211115T012536Z
UID:671-1637665200-1637668800@ccg.ibs.re.kr
SUMMARY:Kyoung-Seog Lee\, Cox Rings and Geometry of Some Surfaces of General Type with pg=q=0
DESCRIPTION:     Speaker\n\n\nKyoung-Seog Lee\nUniversity of Miami\n\n\n\n\n\n\nCox ring is an important tool in modern algebraic geometry and several other branches of mathematics. In the first part of this talk\, I will briefly review basic theory of Cox ring and explain how it connects birational geometry and geometric invariant theory. Then I will discuss how we can use Cox rings to study geometry of certain algebraic surfaces of general type with pg=q=0. The second part of this talk is based on several joint works (some in progress) with JongHae Keum and Davide Frapporti.
URL:https://ccg.ibs.re.kr/event/2021-11-23/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211116T093000
DTEND;TZID=Asia/Seoul:20211116T103000
DTSTAMP:20260417T032259
CREATED:20211116T003000Z
LAST-MODIFIED:20211025T012856Z
UID:669-1637055000-1637058600@ccg.ibs.re.kr
SUMMARY:Giancarlo Urzúa\, Wormholes: MMP\, Topology\, Continued Fractions
DESCRIPTION:     Speaker\n\n\nGiancarlo Urzúa\nPontificia Universidad Catolica de Chile\n\n\n\n\n\n\nWe defined wormholes in https://arxiv.org/abs/2102.02177 (joint with Nicolás Vilches). Conjecturally it is a way to non-continuous travel in the KSBA compactification of the moduli space of surfaces of general type. It depends on a particular MMP. In that paper\, we verified the conjecture in several cases\, but many remain open. Beyond the certainty of the conjecture\, it would be interesting to know about changes in the topology or differential structure after traveling through a wormhole. In this talk\, I will exemplify what we know\, and I will state open questions\, which also include a mysterious combinatorial invariant delta that remains constant in this journey and seems to be part of some particular sequence of integers.
URL:https://ccg.ibs.re.kr/event/2021-11-16/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211111T160000
DTEND;TZID=Asia/Seoul:20211111T170000
DTSTAMP:20260417T032259
CREATED:20211111T070000Z
LAST-MODIFIED:20211103T124854Z
UID:816-1636646400-1636650000@ccg.ibs.re.kr
SUMMARY:Jihun Yum\, Limits of Bergman kernels on a Tower of Coverings of Compact Kähler Manifolds
DESCRIPTION:     Speaker\n\n\nJihun Yum\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nThe Bergman kernel BX\, which is by the definition the reproducing kernel of the space of L2 holomorphic n-forms on a n-dimensional complex manifold X\, is one of the important objects in complex geometry. In this talk\, we observe the asymptotics of the Bergman kernels\, as well as the Bergman metric\, on a tower of coverings. More precisely\, we show that\, for a tower of finite Galois coverings {ϕj : Xj → X} of compact Kähler manifold X converging to an infinite Galois covering ϕ : X~ → X\, the sequence of push-forward Bergman kernels ϕj*BXj locally uniformly converges to ϕ*BX~. Also\, we show that if the canonical line bundle KX~ of X~ is very ample\, then the canonical line bundle KXj of Xj is also very ample for sufficiently large j. This is a joint work with S. Yoo in IBS-CCG.
URL:https://ccg.ibs.re.kr/event/2021-11-11/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211104T110000
DTEND;TZID=Asia/Seoul:20211104T120000
DTSTAMP:20260417T032259
CREATED:20211014T053459Z
LAST-MODIFIED:20211014T053459Z
UID:797-1636023600-1636027200@ccg.ibs.re.kr
SUMMARY:Jie Liu\, Bigness of Tangent Bundles of Fano Manifolds with Zero Dimensional VMRT
DESCRIPTION:     Speaker\n\n\nJie Liu\nInstitute of Mathematics\, AMSS\, CAS\n\n\n\n\n\n\nIt is expected that the bigness of tangent bundle is a quite restrictive property for Fano manifolds\, especially for those of Picard number one. In this talk\, I will present our recent first attempt to tackle this problem. More precise\, we will consider Fano manifolds of Picard number one and having zero-dimensional VMRT\, and it turns out that in this case only the quintic del Pezzo threefold has big tangent bundle. This is based on my recent joint work with Andreas Höring.
URL:https://ccg.ibs.re.kr/event/2021-11-04/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211028T110000
DTEND;TZID=Asia/Seoul:20211028T120000
DTSTAMP:20260417T032259
CREATED:20211028T020000Z
LAST-MODIFIED:20211006T051155Z
UID:790-1635418800-1635422400@ccg.ibs.re.kr
SUMMARY:Feng Shao\, The Bigness of Tangent Bundles of Projective Manifolds
DESCRIPTION:     Speaker\n\n\nFeng Shao\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nLet X be a Fano manifold. While the properties of the anticanonical divisor –KX and its multiples have been studied by many authors\, the positivity of the tangent bundle TX is much more elusive. In this talk\, we give a complete characterization of the pseudoeffectivity and the bigness of TX for del Pezzo surfaces\, hypersurfaces in the projective space and del Pezzo threefolds.
URL:https://ccg.ibs.re.kr/event/2021-10-28/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211026T110000
DTEND;TZID=Asia/Seoul:20211026T120000
DTSTAMP:20260417T032259
CREATED:20211026T020000Z
LAST-MODIFIED:20211012T021831Z
UID:667-1635246000-1635249600@ccg.ibs.re.kr
SUMMARY:Zhi Jiang\, On Syzygies of Abelian Varieties
DESCRIPTION:     Speaker\n\n\nZhi Jiang\nSCMS\, Fudan University\n\n\n\n\n\n\nSyzygies of ample line bundles on abelian varieties have attracted lots of attentions in recent years. People tried to study these geometric objects by different methods\, including Okounkov bodies\, X-methods from MMP\, and generic vanishing theory. We will report some progress on this subject based on the work of Jiang-Pareschi\, Caucci\, and Ito based on cohomological rank functions.
URL:https://ccg.ibs.re.kr/event/2021-10-26/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211014T110000
DTEND;TZID=Asia/Seoul:20211014T120000
DTSTAMP:20260417T032259
CREATED:20211014T020000Z
LAST-MODIFIED:20211005T030302Z
UID:787-1634209200-1634212800@ccg.ibs.re.kr
SUMMARY:Yewon Jeong\, Several Types of Dual Defective Cubic Hypersurfaces
DESCRIPTION:     Speaker\n\n\nYewon Jeong\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nGiven a hypersurface X = V(f) in a complex projective space\, we say X is dual defective if the Gauss map of X\, the restriction of the gradient map of f on X\, has positive dimensional fibers. Especially for cubics\, there is an interesting classification of them. We will study several types of dual defective cubic hypersurfaces and the relation between them.
URL:https://ccg.ibs.re.kr/event/2021-10-14/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211005T110000
DTEND;TZID=Asia/Seoul:20211005T120000
DTSTAMP:20260417T032259
CREATED:20211005T020000Z
LAST-MODIFIED:20210924T092727Z
UID:663-1633431600-1633435200@ccg.ibs.re.kr
SUMMARY:Yuchen Liu\, K-stability and Moduli of Quartic K3 Surfaces
DESCRIPTION:     Speaker\n\n\nYuchen Liu\nNorthwestern University\n\n\n\n\n\n\nWe show that K-moduli spaces of (P3\, cS) where S is a quartic surface interpolates between the GIT moduli space and the Baily-Borel compactification as c varies in (0\,1). We completely describe the wall crossings of these K-moduli spaces. As a consequence\, we verify Laza-O’Grady’s prediction on the Hassett-Keel-Looijenga program for quartic K3 surfaces. This is based on joint work with K. Ascher and K. DeVleming.
URL:https://ccg.ibs.re.kr/event/2021-10-05/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210930T110000
DTEND;TZID=Asia/Seoul:20210930T120000
DTSTAMP:20260417T032259
CREATED:20210930T020000Z
LAST-MODIFIED:20210908T051040Z
UID:660-1632999600-1633003200@ccg.ibs.re.kr
SUMMARY:Yoon-Joo Kim\, The Dual Lagrangian Fibration of Compact Hyper-Kähler Manifolds
DESCRIPTION:     Speaker\n\n\nYoon-Joo Kim\nStony Brook University\n\n\n\n\n\n\nA compact hyper-Kähler manifold is a higher dimensional generalization of a K3 surface. An elliptic fibration of a K3 surface correspondingly generalizes to the so-called Lagrangian fibration of a compact hyper-Kähler manifold. It is known that an elliptic fibration of a K3 surface is always “self-dual” in a certain sense. This turns out to be not the case for higher-dimensional Lagrangian fibrations. In this talk\, we will explicitly construct the dual of Lagrangian fibrations of all currently known examples of compact hyper-Kähler manifolds.
URL:https://ccg.ibs.re.kr/event/2021-09-30/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210916T110000
DTEND;TZID=Asia/Seoul:20210916T120000
DTSTAMP:20260417T032259
CREATED:20210916T020000Z
LAST-MODIFIED:20210826T030047Z
UID:655-1631790000-1631793600@ccg.ibs.re.kr
SUMMARY:Changho Han\, Compact Moduli of Lattice Polarized K3 Surfaces with Nonsymplectic Cyclic Action of Order 3
DESCRIPTION:     Speaker\n\n\nChangho Han\nUniversity of Georgia\n\n\n\n\n\n\nObserve that any construction of “meaningful” compactification of moduli spaces of objects involve enlarging the class of objects in consideration. For example\, Deligne and Mumford introduced the notion of stable curves in order to compactify the moduli of smooth curves of genus g\, and Satake used the periods from Hodge theory to compactify the same moduli space. After a brief review of the elliptic curve case (how those notions are the same)\, I will generalize into looking at various compactifications of Kondo’s moduli space of lattice polarized K3 surfaces (which are of degree 6) with nonsymplectic Z/3Z group action; this involves periods and genus 4 curves by Kondo’s birational period map in 2002. Then\, I will extend Kondo’s birational map to describe birational relations between different compactifications by using the slc compactifications (also known as KSBA compactifications) of moduli of surface pairs. The main advantage of this approach is that we obtain an explicit classification of degenerate K3 surfaces\, which is used to find geometric meaning of points parametrized by Hodge-theoretic compactifications. This comes from joint works (in progress) with Valery Alexeev\, Anand Deopurkar\, and Philip Engel.
URL:https://ccg.ibs.re.kr/event/2021-09-16/
LOCATION:on-line
CATEGORIES:Algebraic Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210819T110000
DTEND;TZID=Asia/Seoul:20210819T120000
DTSTAMP:20260417T032259
CREATED:20210819T020000Z
LAST-MODIFIED:20210803T072832Z
UID:643-1629370800-1629374400@ccg.ibs.re.kr
SUMMARY:Sung Rak Choi\, Subadditivity of Okounkov Bodies
DESCRIPTION:     Speaker\n\n\nSung Rak Choi\nYonsei University\n\n\n\n\n\n\nWe will investigate the subadditivity theorem of Okounkov bodies for algebraic fiber spaces. As an application\, we obtain the subadditivity of the numerical Kodaira dimension and the restricted volume for algebraic fiber spaces. As a byproduct\, we obtain a criterion of birational isotriviality in terms of Okounkov bodies when the general fiber is of general type. As a special case\, we prove some variants of the Iitaka conjecture. We expect that our results will provide a new approach toward the Iitaka conjecture. \nThis is an ongoing research\, in collaboration with Dr. Jinhyung Park.
URL:https://ccg.ibs.re.kr/event/2021-08-19/
LOCATION:on-line
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210812T110000
DTEND;TZID=Asia/Seoul:20210812T120000
DTSTAMP:20260417T032259
CREATED:20210812T020000Z
LAST-MODIFIED:20210803T072821Z
UID:641-1628766000-1628769600@ccg.ibs.re.kr
SUMMARY:Jinhyung Park\, Comparing Numerical Iitaka Dimensions
DESCRIPTION:     Speaker\n\n\nJinhyung Park\nSogang University\n\n\n\n\n\n\nThere are several definitions of the “numerical” Iitaka dimensions of a pseudoeffective divisor\, which are numerical analogues to the Iitaka dimension. Recently\, Lesieutre proved that notions of numerical Iitaka dimensions do not coincide. In this talk\, we prove that many of numerical Iitaka dimensions are equal to the notion introduced by Boucksom-Demailly-Paun-Peternell and that some other invariants introduced by Nakayama and Lehmann can be arbitrarily larger than this notion. We also show some properties of abundant divisors. This is joint work with Sung Rak Choi.
URL:https://ccg.ibs.re.kr/event/2021-08-12/
LOCATION:on-line
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20210712
DTEND;VALUE=DATE:20210717
DTSTAMP:20260417T032259
CREATED:20210708T084051Z
LAST-MODIFIED:20210708T084051Z
UID:627-1626048000-1626479999@ccg.ibs.re.kr
SUMMARY:2021 Pacific Rim Complex and Symplectic Geometry Conference
DESCRIPTION:https://cgp.ibs.re.kr/activities/conferences/337
URL:https://ccg.ibs.re.kr/event/2021-07-12-16/
LOCATION:on-line
CATEGORIES:Conferences and Workshops
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210708T140000
DTEND;TZID=Asia/Seoul:20210708T150000
DTSTAMP:20260417T032259
CREATED:20210622T042954Z
LAST-MODIFIED:20210628T125100Z
UID:608-1625752800-1625756400@ccg.ibs.re.kr
SUMMARY:Yonghwa Cho\, Cohomology of Divisors on Burniat Surfaces
DESCRIPTION:     Speaker\n\n\nYonghwa Cho\nKIAS\n\n\n\n\n\n\nA (primary) Burniat surface is a complex surface of general type that can be obtained as a bidouble cover of del Pezzo surface with K2 = 6. The Picard group is an abelian group of rank 4 with torsion part isomorphic to (Z/2)6. Alexeev studied the divisors on Burniat surfaces\, and observed that the irreducible components of ramification divisors span the semigroup of effective divisors. Based on Alexeev’s result\, I will describe the method for computing cohomology of arbitrary divisors on Burniat surfaces. If time permits\, (non-)existence question about Ulrich bundles will be discussed as an application.
URL:https://ccg.ibs.re.kr/event/2021-07-08-1400/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
END:VCALENDAR