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PRODID:-//Center for Complex Geometry - ECPv6.15.20//NONSGML v1.0//EN
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X-WR-CALNAME:Center for Complex Geometry
X-ORIGINAL-URL:https://ccg.ibs.re.kr
X-WR-CALDESC:Events for Center for Complex Geometry
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20190101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210930T110000
DTEND;TZID=Asia/Seoul:20210930T120000
DTSTAMP:20260417T081116
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:20260417T081116
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:20260417T081116
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:20260417T081116
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:20260417T081116
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:20260417T081116
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
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210708T110000
DTEND;TZID=Asia/Seoul:20210708T120000
DTSTAMP:20260417T081116
CREATED:20210622T042608Z
LAST-MODIFIED:20210622T042608Z
UID:605-1625742000-1625745600@ccg.ibs.re.kr
SUMMARY:Sukmoon Huh\, Logarithmic Sheaves on Projective Surfaces
DESCRIPTION:     Speaker\n\n\nSukmoon Huh\nSungkyunkwan University\n\n\n\n\n\n\nA logarithmic sheaf is a sheaf of differential one-forms on a variety with logarithmic poles along a given divisor. One of the main problems on this object is to see whether Torelli property holds\, i.e. whether two different divisors define two non-isomorphic logarithmic sheaves. In this talk\, after reviewing some basic material\, we are going to introduce two new approaches to obtain Torelli property. This is a joint work in progress with S. Marchesi\, J. Pons-Llopis and J. Valles.
URL:https://ccg.ibs.re.kr/event/2021-07-08/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210701T110000
DTEND;TZID=Asia/Seoul:20210701T120000
DTSTAMP:20260417T081116
CREATED:20210622T042251Z
LAST-MODIFIED:20210623T042117Z
UID:601-1625137200-1625140800@ccg.ibs.re.kr
SUMMARY:Yong Hu\, Noether-Severi Inequality and Equality for Irregular Threefolds of General Type
DESCRIPTION:     Speaker\n\n\nYong Hu\nKIAS\n\n\n\n\n\n\nFor complex smooth irregular 3-folds of general type\, I will introduce the optimal Noether-Severi inequality. This answers an open question of Zhi Jiang in dimension three. Moreover\, I will also completely describe the canonical models of irregular 3-folds attaining the Noether-Severi equality. This is a joint work with Tong Zhang.
URL:https://ccg.ibs.re.kr/event/2021-07-01/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210623T160000
DTEND;TZID=Asia/Seoul:20210623T170000
DTSTAMP:20260417T081116
CREATED:20210618T071309Z
LAST-MODIFIED:20210623T023313Z
UID:598-1624464000-1624467600@ccg.ibs.re.kr
SUMMARY:Pak Tung Ho\, Chern-Yamabe Problem
DESCRIPTION:     Speaker\n\n\nPak Tung Ho\nSogang University\n\n\n\n\n\n\nI will explain what the Chern-Yamabe problem is\, and talk about the Chern-Yamabe flow which is a geometric flow approach to solve the Chern-Yamabe problem. \nI will also mention other results related to the Chern-Yamabe problem.
URL:https://ccg.ibs.re.kr/event/2021-06-23/
LOCATION:on-line
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210617T110000
DTEND;TZID=Asia/Seoul:20210617T120000
DTSTAMP:20260417T081116
CREATED:20210520T034412Z
LAST-MODIFIED:20210615T082915Z
UID:504-1623927600-1623931200@ccg.ibs.re.kr
SUMMARY:Baohua Fu\, Normalized Tangent Bundle\, Pseudoeffective Cone and Varieties with Small Codegree
DESCRIPTION:     Speaker\n\n\nBaohua Fu\nChinese Academy of Science\n\n\n\n\n\n\nWe propose a conjectural list of Fano manifolds of Picard number one whose normalized tangent bundle is pseudoeffective and we prove it in various situations by relating it to the complete divisibility conjecture of Russo and Zak on varieties with small codegrees. The pseudoeffective cone of the projectivized tangent bundle of a rational homogeneous space of Picard number one is explicitly determined by studying the total dual VMRT and the geometry of stratified Mukai flops. This is a joint work with Jie LIU.
URL:https://ccg.ibs.re.kr/event/2021-06-17/
LOCATION:on-line
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210616T160000
DTEND;TZID=Asia/Seoul:20210616T170000
DTSTAMP:20260417T081116
CREATED:20210602T045950Z
LAST-MODIFIED:20210602T045950Z
UID:524-1623859200-1623862800@ccg.ibs.re.kr
SUMMARY:Dano Kim\, Canonical Bundle Formula and Degenerating Families of Volume Forms
DESCRIPTION:     Speaker\n\n\nDano Kim\nDepartment of Mathematical Sciences\, Seoul National University\n\n\n\n\n\n\nWe will talk about a metric version of Kawamata’s canonical bundle formula for log Calabi-Yau fibrations: the L2 metric carries singularity described by the discriminant divisor and the moduli part line bundle has a singular hermitian metric with vanishing Lelong numbers. This answers a folklore conjecture arising from work of Kawamata and Tsuji and a question of Eriksson\, Freixas i Montplet and Mourougane. It has immediate applications to L2 extension theorems which was our starting point.
URL:https://ccg.ibs.re.kr/event/2021-06-16/
LOCATION:on-line
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210603T110000
DTEND;TZID=Asia/Seoul:20210603T120000
DTSTAMP:20260417T081116
CREATED:20210518T033401Z
LAST-MODIFIED:20210518T033401Z
UID:496-1622718000-1622721600@ccg.ibs.re.kr
SUMMARY:Joonyeong Won\, K-stability\, Kähler-Einstein Metric on Fano Varieties and Sasaki-Einstein Metric on 5-dimensional Smale Manifolds
DESCRIPTION:     Speaker\n\n\nJoonyeong Won\nKIAS\n\n\n\n\n\n\nWe discuss on recent progresses of the existence problem of Kähler-Einstein metric on Fano varieties by K-stability of them and also the existence problem of Sasaki-Einstein metric on 5-dimensional Smale manifolds via K-stability of weighted hypersurface log del Pezzo surfaces.
URL:https://ccg.ibs.re.kr/event/2021-06-03/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210602T160000
DTEND;TZID=Asia/Seoul:20210602T170000
DTSTAMP:20260417T081116
CREATED:20210524T074057Z
LAST-MODIFIED:20210524T074057Z
UID:506-1622649600-1622653200@ccg.ibs.re.kr
SUMMARY:Hoseob Seo\, On Singularities of Toric Plurisubharmonic Funcitons
DESCRIPTION:     Speaker\n\n\nHoseob Seo\nResearch Institute of Mathematics\, Seoul National University\n\n\n\n\n\n\nIn this talk\, we discuss recent progresses on singularities of toric plurisubharmonic functions. First\, we review the notion of Newton convex bodies of toric plurisubharmonic functions on a polydisk D(0\,r) ⊂ Cn. As an application\, we show that the cluster points of jumping numbers of J(φ)0 are not accumulated and give a precise characterization of the set of those cluster points. These generalize a recent result of Kim and Seo from n = 2. \nOn the other hand\, we extends a result by Guan\, which proved when toric plurisubharmonic functions of the form log(∑ |z|ai) have a decreasing equisingular approximation with analytic singularities. We give a criterion for the existence of a decreasing equisingular toric approximation with analytic singularities for a given toric plurisubharmonic function. This is a joint work with Jongbong An.
URL:https://ccg.ibs.re.kr/event/2021-06-02/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210527T110000
DTEND;TZID=Asia/Seoul:20210527T120000
DTSTAMP:20260417T081116
CREATED:20210430T040608Z
LAST-MODIFIED:20210430T042430Z
UID:443-1622113200-1622116800@ccg.ibs.re.kr
SUMMARY:Lucas Kaufmann\, Commuting Pairs of Endomorphisms
DESCRIPTION:     Speaker\n\n\nLucas Kaufmann\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nThe study of functional equations is at the origin of the early developments of the iteration theory of polynomials and rational functions\, carried out by Fatou\, Julia\, Ritt and others. Among these equations\, the commutation relation f g = g f is particularly interesting. In this talk I will discuss the following problem: can we classify commuting pairs of holomorphic endomorphisms of the complex projective space? \nWe will see that the relation f g = g f gives rise to special symmetries of several dynamical objects attached to these maps\, such as their invariant currents and measures\, their Julia sets and so on. This rigidity allows us to understand the structure of these maps and even give a full description in low dimensions.
URL:https://ccg.ibs.re.kr/event/2021-05-27/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210520T110000
DTEND;TZID=Asia/Seoul:20210520T120000
DTSTAMP:20260417T081116
CREATED:20210430T040140Z
LAST-MODIFIED:20210430T042439Z
UID:437-1621508400-1621512000@ccg.ibs.re.kr
SUMMARY:Lucas Kaufmann\, Introduction to Dynamics in Several Complex Variables
DESCRIPTION:     Speaker\n\n\nLucas Kaufmann\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nThe field of complex dynamics deals with the study of the iteration of a map from a complex manifold to itself. The one dimensional theory is more than one-hundred years old and is now very well developed. \nDue to the fundamental differences between complex analysis in one and higher dimensions\, the study of higher dimensional dynamical systems is much more recent and is still an active research domain\, with interesting connections to complex geometry\, algebraic geometry\, number theory\, mathematical physics etc. \nThe aim of this talk is to survey standard results on the dynamics of self-maps in complex manifolds. I will focus on the case of endomorphisms of the complex projective space and use it to illustrate how the tools of pluripotential theory and the theory of currents are crucial in their study. \nIn particular\, I aim to talk about Green currents and measures\, equidistribution theorems and\, if time permits\, relations with the intersection theory of currents.
URL:https://ccg.ibs.re.kr/event/2021-05-20/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210513T110000
DTEND;TZID=Asia/Seoul:20210513T120000
DTSTAMP:20260417T081116
CREATED:20201120T045532Z
LAST-MODIFIED:20210430T041419Z
UID:216-1620903600-1620907200@ccg.ibs.re.kr
SUMMARY:Jeong-Seop Kim\, Stability of Symmetric Powers of Vector Bundles on a Curve
DESCRIPTION:     Speaker\n\n\nJeong-Seop Kim\nKAIST\n\n\n\n\n\nFor a stable vector bundle E on a smooth projective curve\, it is known that the symmetric powers Sk E are semi-stable and are stable for all k > 0 in sufficiently general. Moreover\, if E has rank 2\, then Sk E is destabilized by a line subbundle if and only if the ruled surface PC(E) admits a k-section of zero self-intersection. In this talk\, concentrating on the case of rank 2\, we will find answers to the questions of which E has strictly semi-stable Sk E\, and how many such E there are. Also\, we will introduce relations between such E and the orthogonal bundles when k = 2\, and Nori’s finite bundles when k ≥ 3.
URL:https://ccg.ibs.re.kr/event/2020-12-17/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210512T160000
DTEND;TZID=Asia/Seoul:20210512T170000
DTSTAMP:20260417T081116
CREATED:20210506T041021Z
LAST-MODIFIED:20210506T041021Z
UID:492-1620835200-1620838800@ccg.ibs.re.kr
SUMMARY:Young-jun Choi\, Existence of a Complete Holomorphic Vector Field via the Kähler-Einstein Metric
DESCRIPTION:     Speaker\n\n\nYoung-jun Choi\nPusan National University\n\n\n\n\n\n\nA fundamental problem in Several Complex Variables is to classify bounded pseudoconvex domains in the complex Euclidean space with a noncompact automorphism group\, especially with a compact quotient. In the results of Wong-Rosay and Frankel\, they make use of the “Scaling method” for obtaining an 1-parameter family of automorphisms\, which generates a holomorphic vector field. \nIn this talk\, we discuss the existence of a nowhere vanishing complete holomorphic vector field on a strongly pseudoconvex manifold admitting a negatively curved Kähler-Einstein metric and discrete sequence of automorphisms by introducing the scaling method on potentials of the Kähler-Einstein metric. \nThis is a joint work with Kang-Hyurk Lee in Gyenongsang National University.
URL:https://ccg.ibs.re.kr/event/2021-05-12/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210422T110000
DTEND;TZID=Asia/Seoul:20210422T120000
DTSTAMP:20260417T081116
CREATED:20210312T041646Z
LAST-MODIFIED:20210430T041501Z
UID:341-1619089200-1619092800@ccg.ibs.re.kr
SUMMARY:Hosung Kim\, The Space of Rational Curves on a General Hypersurface of Projective Space
DESCRIPTION:     Speaker\n\n\nHosung Kim\nIBS\, Center for Complex Geometry\n\n\n\n\n\nIn 1979\, the work of Mori had brought out the importance of the study of rational curves in higher-dimensional geometry. In 1990s\, applying Mori’s bend-and-break method\, Campana and Kollar-Miyaoka-Mori proved that any Fano manifold is rationally connected. Since then the family of raional curves on Fano maniflolds has been considerably studied especially about the dimension and irreducibility. The expected dimension of the family of rational curves of degree e in a hypersurface of degree d in Pn is e(n-d+1)+n-4\, and it has been conjectured that this family is irreducible and has dimension of the expected dimension if d ≤ n-1 and n > 3. This conjecture has been proven for d ≤ n-2 and e arbitrary by Riedl and Yang in 2019 based on bend-and-break. For d = n-1\, some results for low e were obtained by Tseng in 2017. In this seminar I am going to introduce a technique based on degenerating the ambient projective space to a 2-component fan and simultaneously degenerate a general hypersurface of a projective space to a subscheme of the fan. Using this method\, Ziv Ran reduced the original problem to that on the space of rational curves in Pn which are some secant to a certain (d\,d-1) complete intersection\, and proved the cases when e < d ≤ n-1 and n > 4.
URL:https://ccg.ibs.re.kr/event/2021-04-22/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210421T160000
DTEND;TZID=Asia/Seoul:20210421T170000
DTSTAMP:20260417T081116
CREATED:20210409T050246Z
LAST-MODIFIED:20210430T041516Z
UID:417-1619020800-1619024400@ccg.ibs.re.kr
SUMMARY:Taeyong Ahn\, Positive Closed Currents and Super-potentials
DESCRIPTION:     Speaker\n\n\nTaeyong Ahn\nInha University\, Department of Mathematics Education\n\n\n\n\n\nIn this talk\, we briefly review the notion and properties of positive closed currents and super-potentials. As an application\, we discuss the equidistribution of positive closed currents on the projective space. We also discuss the difficulty of the extension of the result to a general compact Kähler manifold.
URL:https://ccg.ibs.re.kr/event/2021-04-21/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210415T110000
DTEND;TZID=Asia/Seoul:20210415T120000
DTSTAMP:20260417T081116
CREATED:20210312T042356Z
LAST-MODIFIED:20210430T041530Z
UID:348-1618484400-1618488000@ccg.ibs.re.kr
SUMMARY:Seungjae Lee\, L2 Extension of Holomorphic Jets on Complex Hyperbolic Forms
DESCRIPTION:     Speaker\n\n\nSeungjae Lee\nIBS\, Center for Complex Geometry\n\n\n\n\n\nAs the continuation of the previous talk\, I discuss an L2 extension problem of holomorphic jets on compact complex hyperbolic forms. Let Γ be a cocompact torsion-free lattice in the automorphism group Aut(Bn) and Ω be a quotient Bn × Bn given by diagonal action of Γ. In the setting\, Ω becomes a ball-fiber bundle over Σ = Bn / Γ. Since we can identify symmetric differentials on Σ and jets of holomorphic function on D which is the maximal compact analytic variety on Ω\, it is natural to expect that holomorphic function on Ω can be derived by symmetric differentials. In this context\, M. Adachi (2017) extends holomorphic jets on D to weighted L2 holomorphic functions on Σ for the n=1 case. In 2020\, A. Seo and S. Lee generalized his result by developing a Hodge type identity on SmTΣ*. In this talk\, I will explain recent progress and if time is permitted\, I sketch the proof of our result. This is joint work with A. Seo.
URL:https://ccg.ibs.re.kr/event/2021-04-15/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210408T110000
DTEND;TZID=Asia/Seoul:20210408T120000
DTSTAMP:20260417T081116
CREATED:20210226T055225Z
LAST-MODIFIED:20210430T041740Z
UID:312-1617879600-1617883200@ccg.ibs.re.kr
SUMMARY:Seungjae Lee\, Symmetric Differentials on Complex Hyperbolic Forms
DESCRIPTION:     Speaker\n\n\nSeungjae Lee\nIBS\, Center for Complex Geometry\n\n\n\n\n\nLet Γ be a cocompact torsion-free lattice in the automorphism group of complex unit ball Bn\, Aut(Bn). In this talk\, we discuss the existence of symmetric differentials on the compact ball quotient Σ = Bn / Γ. Since Σ has a Kähler metric induced by the Bergman metric on the complex unit ball Bn\, it has symmetric differentials on SmTΣ* if m is sufficiently large. Unfortunately\, finding the smallest degree m which guarantees a symmetric differential on SmTΣ* is difficult in even compact ball quotient cases. Instead of this\, I will prove that m ≥ n+2 is a sufficient condition to give a symmetric differential on SmTΣ*. To achieve this goal\, I will explain how to induce symmetric differentials by using a recursive formula for ∂-operators and Poincaré series. This is joint work with A. Seo.
URL:https://ccg.ibs.re.kr/event/2021-04-08/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210407T160000
DTEND;TZID=Asia/Seoul:20210407T180000
DTSTAMP:20260417T081116
CREATED:20210317T024334Z
LAST-MODIFIED:20210430T041731Z
UID:384-1617811200-1617818400@ccg.ibs.re.kr
SUMMARY:Jihun Yum\,  Characterization of Diederich-Fornaess and Steinness Indices in Complex Manifolds
DESCRIPTION:     Speaker\n\n\nJihun Yum\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nLet Ω be a relatively compact pseudoconvex domain in a complex manifold X with smooth boundary ∂Ω. The Diederich-Fornaess index and the Steinness index of Ω are defined by \nDF(Ω) := supρ { 0 < η < 1 : -(-ρ)η is strictly plurisubharmonic on Ω ∩ U for some neighborhood U of ∂Ω }\, \nS(Ω) := infρ { η > 1 : ρη is strictly plurisubharmonic on Ωc ∩ U for some neighborhood U of ∂Ω }\, \nwhere ρ is a defining function for Ω. \nIn the previous talk\, we have seen that two indices are completely characterized by D’Angelo 1-form when the ambient space is X = Cn. In this talk\, we generalize the formulas for a relatively compact pseudoconvex domains in a (general) complex manifold X. Since the formulas do not hold anymore in general\, unfortunately\, we introduce 4 kinds of each of the Diederich-Fornaess and Steinness indices. Then we give some non-degeneracy conditions for these indices agree. Also\, we exam the geometric meaning of the D’Angelo 1-form when the boundary ∂Ω is Levi-flat.
URL:https://ccg.ibs.re.kr/event/2021-04-07/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210401T110000
DTEND;TZID=Asia/Seoul:20210401T120000
DTSTAMP:20260417T081116
CREATED:20210312T041527Z
LAST-MODIFIED:20210430T041721Z
UID:339-1617274800-1617278400@ccg.ibs.re.kr
SUMMARY:Qifeng Li\, Rigidity of Wonderful Group Compactifications under Fano Deformations
DESCRIPTION:     Speaker\n\n\nQifeng Li\nIBS\, Center for Complex Geometry\n\n\n\n\n\nFor a complex connected semisimple linear algebraic group G of adjoint type and of rank n\, De Concini and Procesi constructed its wonderful compactification X\, which is a smooth Fano variety of Picard number n enjoying many interesting properties. In this talk\, we will show that the wonderful compactification X is rigid under Fano deformations. Namely\, for any family of smooth Fano varieties over a connected base\, if one fiber is isomorphic to X\, then so are all other fibers. This answers a question raised by Bien and Brion in their work on the local rigidity of wonderful varieties.
URL:https://ccg.ibs.re.kr/event/2021-04-01/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210325T110000
DTEND;TZID=Asia/Seoul:20210325T120000
DTSTAMP:20260417T081116
CREATED:20210312T041405Z
LAST-MODIFIED:20210430T041707Z
UID:337-1616670000-1616673600@ccg.ibs.re.kr
SUMMARY:Sungmin Yoo\, Bergman Metrics and Kähler-Einstein Metrics on Projective Manifolds
DESCRIPTION:     Speaker\n\n\nSungmin Yoo\nIBS\, Center for Complex Geometry\n\n\n\n\n\nAfter Yau suggested the problem of approximations of Kähler-Einstein metrics by Bergman type metrics\, various types of Bergman metrics have been developed and studied by Tian\, Donaldson\, Tsuji\, etc. They showed that if a polarized manifold admits a Kähler-Einstein metric\, there exist a sequence of Bergman type metrics which converges to the Kähler-Einstein metric. In this talk\, we will survey their results and discuss some remaining problems in this subject.
URL:https://ccg.ibs.re.kr/event/2021-03-25/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210324T160000
DTEND;TZID=Asia/Seoul:20210324T180000
DTSTAMP:20260417T081116
CREATED:20210315T051658Z
LAST-MODIFIED:20210430T041807Z
UID:363-1616601600-1616608800@ccg.ibs.re.kr
SUMMARY:Jihun Yum\, Characterization of Diederich-Fornaess and Steinness Indices in Cn
DESCRIPTION:     Speaker\n\n\nJihun Yum\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nLet Ω be a bounded pseudoconvex domain in Cn with smooth boundary ∂Ω. The Diederich-Fornaess index and the Steinness index of Ω are defined by \nDF(Ω) := supρ { 0 < η < 1 : -(-ρ)η is strictly plurisubharmonic on Ω ∩ U for some neighborhood U of ∂Ω }\, \nS(Ω) := infρ { η > 1 : ρη is strictly plurisubharmonic on Ωc ∩ U for some neighborhood U of ∂Ω }\, \nwhere ρ is a defining function for Ω. \nFirst\, we see basic properties and known results about the Diederich-Fornaess and Steinness indices. Also\, we see the relation between two indices on a 1-parameter family of domains in C2\, called worm domains\, constructed by Diederich and Fornaess. \n\nWe characterize the Diederich-Fornaess and Steinness indices in terms of a special 1-form\, which we call D’Angelo 1-form. These formulas are the most important in this talk. After giving a sketch of the proof\, we show many applications and corollaries of the formulas. Especially\, we prove that \n\n\n\ntwo indices are invariant under CR-diffeomorphisms\,\nsemi-continuity of two indices.
URL:https://ccg.ibs.re.kr/event/2021-03-24/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210318T110000
DTEND;TZID=Asia/Seoul:20210318T120000
DTSTAMP:20260417T081116
CREATED:20210226T055012Z
LAST-MODIFIED:20210430T041824Z
UID:310-1616065200-1616068800@ccg.ibs.re.kr
SUMMARY:Sungmin Yoo\, Fiberwise Kähler-Ricci Flows on Families of Strongly Pseudoconvex Domains
DESCRIPTION:     Speaker\n\n\nSungmin Yoo\nIBS\, Center for Complex Geometry\n\n\n\n\n\nA study on the positive variation of Kähler-Einstein metrics is first developed by Schumacher. More precisely\, he has proved that the fiberwise Kähler-Einstein metrics on a family of canonically polarized compact Kähler manifolds is positive-definite on the total space. Later\, Berman constructed the fiberwise Kähler-Ricci flow which converges to the fiberwise Kähler-Einstein metrics and showed that the positivity is preserved under this flow. In this talk\, I will explain how to generalize these to a family of bounded strongly pseudoconvex domains\, which is an important examples of non-compact complete Kähler manifolds. This is joint work with Young-Jun Choi.
URL:https://ccg.ibs.re.kr/event/2021-03-18/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210128T110000
DTEND;TZID=Asia/Seoul:20210128T120000
DTSTAMP:20260417T081116
CREATED:20210108T061352Z
LAST-MODIFIED:20210430T041909Z
UID:283-1611831600-1611835200@ccg.ibs.re.kr
SUMMARY:Hyungryul Baik\, Limits of Canonical Metrics in Low-dimensions
DESCRIPTION:     Speaker\n\n\nHyungryul Baik\nKAIST\n\n\n\n\n\nFor a tower of finite normal covers of graphs or surfaces\, one can consider a sequence of metrics on the base given by pull-back of canonical metric of the covers. We show that such a sequence has a limit and it depends only on the cover approximated by the tower up to scaling. The case of compact Riemann surface where the tower approximates the universal cover is due to Kazhdan. In this talk\, I will explain why one might be interested in such a problem\, give a brief introduction to the main tool – L2-theory\, and discuss some future directions. This talk is based on a joint work with Farbod Shokrieh and Chenxi Wu.
URL:https://ccg.ibs.re.kr/event/2021-01-28/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210121T110000
DTEND;TZID=Asia/Seoul:20210121T120000
DTSTAMP:20260417T081116
CREATED:20210108T061009Z
LAST-MODIFIED:20210430T041929Z
UID:280-1611226800-1611230400@ccg.ibs.re.kr
SUMMARY:Seung-Jo Jung\, Hodge Ideals and Spectra of Hypersurface Singularities
DESCRIPTION:     Speaker\n\n\nSeung-Jo Jung\nJeonbuk National University\n\n\n\n\n\nRecently Mustata-Popa introduced a generalisation of multiplier ideals\, which is called Hodge ideals. This talk introduces the Hodge ideals and explains the relations with other invariants\, e.g. Bernstein-Sato polynomials\, Hodge spectra\, log canonical thresholds\, minimal exponents etc. Mainly this talk concerns the relation between Hodge ideals and Hodge spectra. This talk is based on the joint paper with I-K. Kim\, M. Saito\, and Y. Yoon.
URL:https://ccg.ibs.re.kr/event/2021-01-21/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210114T160000
DTEND;TZID=Asia/Seoul:20210114T170000
DTSTAMP:20260417T081116
CREATED:20201229T040801Z
LAST-MODIFIED:20210430T041948Z
UID:276-1610640000-1610643600@ccg.ibs.re.kr
SUMMARY:Sangbum Yoo\, Spectral Data for Principal Higgs Bundles over a Singular Curve
DESCRIPTION:     Speaker\n\n\nSangbum Yoo\nGongju National University of Education\n\n\n\n\n\n\nSpectral data for Higgs bundles over a smooth curve has been studied by several mathematicians. The studies in this direction are originated by N.J.Hitchin. Specially\, it has contributed to the studies on the fibers of the Hitchin map. In this talk\, I will introduce spectral data for Higgs bundles over a smooth curve and over a singular curve\, and then present my ongoing project about spectral data for principal Higgs bundles over a singular curve.
URL:https://ccg.ibs.re.kr/event/2021-01-14/
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:20260417T081116
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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END:VCALENDAR