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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:20220101T000000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20231016T160000
DTEND;TZID=Asia/Seoul:20231016T170000
DTSTAMP:20231212T062851
CREATED:20231010T015627Z
LAST-MODIFIED:20231010T015627Z
UID:2584-1697472000-1697475600@ccg.ibs.re.kr
SUMMARY:Gil Bor\, Bicycle Tracks\, their Monodromy Invariants and Geodesics
DESCRIPTION: Speaker\n\n\nGil Bor\nCIMAT\n\n\n\n\n\n\nAt first sight\, the pair of front and back wheel tracks left by a passing bike on a sandy or muddy terrain seems like a random pair of curves. This is not the case. For example\, one can usually distinguish between the front and back wheel tracks\, and even the direction at which these were traversed\, based solely on their shapes. You can try it for the following pair of paths. \n \nAnother example: If the front wheel traverses a small enough closed path (compared to the bike size)\, then\, typically\, the back track does not close up\, by an amount approximated by the area enclosed by the front track and the bicycle length; this fact was utilized to build a simple area measuring mechanical device\, now obsolete\, called the Hatchet planimeter. \nIn recent years the subject has attracted attention due to newly discovered relations with the theory of completely integrable systems (the filament flow)\, sub-Riemannian geometry and elasticity theory. I will try to describe some of these developments and open questions.
URL:https://ccg.ibs.re.kr/event/2023-10-16-1600-1700/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20231016T110000
DTEND;TZID=Asia/Seoul:20231016T120000
DTSTAMP:20231212T062851
CREATED:20231010T015222Z
LAST-MODIFIED:20231010T015241Z
UID:2580-1697454000-1697457600@ccg.ibs.re.kr
SUMMARY:Gil Bor\, Cusps of Caustics by Reflection in a Convex Billiard Table
DESCRIPTION: Speaker\n\n\nGil Bor\nCIMAT\n\n\n\n\n\n\nPlace a point light source inside a smooth convex billiard table (or mirror). The n-th caustic by reflection is the envelope of light rays after n reflections. Theorem: each of these caustics\, for a generic point light source\, has at least 4 cusps. Conjecture: there are exactly 4 cusps iff the table is an ellipse. Here are the 2nd\, 5th and 8th caustics by reflection in an ellipse\, each with 4 cusps (marked by gray disks; the light source is the white disk) \n \nThis is a billiard version of “Jacobi’s Last Geometric Statement”\, concerning the number of cusps of the conjugate locus of a point on a convex surface\, proved so far only in the n=1 case. (Joint work with Serge Tabachnikov\, from Penn State\, USA).
URL:https://ccg.ibs.re.kr/event/2023-10-16-1100-1200/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230921T150000
DTEND;TZID=Asia/Seoul:20230921T160000
DTSTAMP:20231212T062851
CREATED:20230905T122128Z
LAST-MODIFIED:20230905T122128Z
UID:2506-1695308400-1695312000@ccg.ibs.re.kr
SUMMARY:Yaoxiong Wen\, Generalized Quiver Mutation and PAX/PAXY Models
DESCRIPTION: Speaker\n\n\nYaoxiong Wen\nKIAS\n\n\n\n\n\n\nDuring this presentation\, I will discuss the generalized quiver mutation conjecture proposed by Prof. Ruan. Our focus will be on proving this conjecture for the Grassmannian bundle. Additionally\, we will explore the determinantal variety and its two different desingularizations\, known as PAX/PAXY models. We will demonstrate the relationship between these models through generalized quiver mutation and prove the PAX/PAXY correspondence in the level of quasimap I-functions. This talk is based on the ongoing research collaboration with Mark Shoemaker and Nathan Priddis.
URL:https://ccg.ibs.re.kr/event/2023-09-21/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230908T110000
DTEND;TZID=Asia/Seoul:20230908T120000
DTSTAMP:20231212T062851
CREATED:20230731T073447Z
LAST-MODIFIED:20230904T004225Z
UID:2414-1694170800-1694174400@ccg.ibs.re.kr
SUMMARY:Fabrizio Catanese\, [IBS-KAIST Seminar] Geometry and Dynamics of Geometric Endomorphisms of the Hesse Moduli Space of Elliptic Curves
DESCRIPTION: Speaker\n\n\nFabrizio Catanese\nUniversity of Bayreuth\n\n\n\n\n\n\nWe consider the geometric map C\, called Cayleyan\, associating to a plane cubic E the adjoint of its dual curve. We show that C and the classical Hessian map H generate a free semigroup. We begin the investigation of the geometry and dynamics of these maps\, and of the geometrically special elliptic curves: these are the elliptic curves isomorphic to cubics in the Hesse pencil which are fixed by some endomorphism belonging to the semigroup generated by H\, C. We point out how the dynamic behaviours of H and C differ drastically. Firstly\, concerning the number of real periodic points: for H these are infinitely many\, for C they are just 4. Secondly\, the Julia set of H is the whole projective line\, unlike what happens for all elements of the semigroup which are not iterates of H.
URL:https://ccg.ibs.re.kr/event/2023-09-08/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230907T150000
DTEND;TZID=Asia/Seoul:20230907T160000
DTSTAMP:20231212T062851
CREATED:20230731T073302Z
LAST-MODIFIED:20230731T084230Z
UID:2410-1694098800-1694102400@ccg.ibs.re.kr
SUMMARY:Yum-Tong Siu\, [IBS-KAIST Seminar] Differential Relations for Multiplier Ideal Sheaves in ∂ Estimates
DESCRIPTION: Speaker\n\n\nYum-Tong Siu\nHarvard University\n\n\n\n\n\n\nFor sums of squares of real vector fields\, Hörmander linked subelliptic estimates to the spanning property of iterated Lie brackets of vector fields. Kohn studied the more complicated analogue of subelliptic ∂ estimates for weakly pseudoconvex domains\, with vector-valued unknowns. \nIn the weak-solution approach to solving the ∂ equation\, multipliers for the test function are introduced so that estimates hold after multiplication by a multiplier. Kohn used the dual formulation of differential forms instead of vector fields so that (i) the Lie brackets of vector fields are replaced by differential relations to generate new multipliers and (ii) the spanning property of iterated Lie brackets is replaced by the constant function 1 being a multiplier. \nWe will focus on recent problems and results concerning Kohn’s theory of subelliptic estimates in terms of D’Angelo’s condition of finite type. The distant eventual goal is to explore the theory for differential relations to generate multipliers for subelliptic estimates for a general system of equations with compatibility conditions.
URL:https://ccg.ibs.re.kr/event/2023-09-07-1500-1600/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230907T110000
DTEND;TZID=Asia/Seoul:20230907T120000
DTSTAMP:20231212T062851
CREATED:20230731T072556Z
LAST-MODIFIED:20230802T012652Z
UID:2408-1694084400-1694088000@ccg.ibs.re.kr
SUMMARY:Thomas Peternell\, Semipositive Tangent Bundles and Canonical Extensions
DESCRIPTION: Speaker\n\n\nThomas Peternell\nUniversity of Bayreuth\n\n\n\n\n\n\nGiven a projective complex manifold M with an ample polarization there is canonically associated an affine bundle Z over M. The question I will discuss is under which circumstances Z is an affine variety\, or at least Stein. This is related to the global structure of M\, specifically to the semipositivity of the tangent bundle. I will explain the main conjectures and recent results (joint work with A. Höring).
URL:https://ccg.ibs.re.kr/event/2023-09-07-1100-1200/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230906T110000
DTEND;TZID=Asia/Seoul:20230906T120000
DTSTAMP:20231212T062851
CREATED:20230731T072411Z
LAST-MODIFIED:20230731T072411Z
UID:2406-1693998000-1694001600@ccg.ibs.re.kr
SUMMARY:George Hitching\, Brill-Noether Loci on Moduli Space of Symplectic Bundles over a Curve
DESCRIPTION: Speaker\n\n\nGeorge Hitching\nOslo Metropolitan University\n\n\n\n\n\n\nLet C be a smooth projective curve of genus g. The symplectic Brill-Noether locus S(k\, 2n\, K) parametrises stable bundles of rank 2n over C with at least k independent sections\, and which admit a nondegenerate skewsymmetric bilinear form with values in the canonical bundle K. This is a symmetric determinantal variety whose tangent spaces are described by a symmetrised Petri map. We show for many values of g\, n and k that S(k\, 2n\, K) is nonempty and has a component which is generically smooth and of the expected dimension. As an application\, we show that for certain n and k\, for any curve of large genus the usual Brill-Noether locus B(k\, 2n\, 2n(g-1)) has a component of excess dimension. This is joint work with Ali Bajravani (Tabriz/Berlin).
URL:https://ccg.ibs.re.kr/event/2023-09-06/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230808T150000
DTEND;TZID=Asia/Seoul:20230808T163000
DTSTAMP:20231212T062851
CREATED:20230720T004618Z
LAST-MODIFIED:20230720T004618Z
UID:2377-1691506800-1691512200@ccg.ibs.re.kr
SUMMARY:Kyeong-Dong Park\, K-stability of Fano Spherical Varieties\, III
DESCRIPTION: Speaker\n\n\nKyeong-Dong Park\nGyeongsang National University\n\n\n\n\n\n\nThe aim of this seminar is to provide participants with a comprehensive understanding of the paper “K-stability of Fano spherical varieties” by Thibaut Delcroix. For a reductive algebraic group G\, a normal G-variety is called spherical if it contains an open B-orbit\, where B is a fixed Borel subgroup of G. The class of spherical varieties contains several important families which were studied independently\, for example\, toric varieties\, rational homogeneous varieties\, group embeddings\, horospherical varieties\, symmetric varieties\, and wonderful varieties. They are classified by combinatorial objects called colored fans\, which generalize the fans appearing in the classification of toric varieties. We discuss Delcroix’s combinatorial criterion for K-stability of a smooth Fano spherical variety in terms of the barycenter of its moment polytope with respect to the Duistermaat-Heckman measure and data associated to the corresponding spherical homogeneous space. \n(1) Spherical varieties\, colored fans\, and algebraic moment polytopes \n(2) Criterion for K-stability of Fano spherical varieties and its applications \n(3) Equivariant test configurations with horospherical central fiber\, and modified Futaki invariant
URL:https://ccg.ibs.re.kr/event/2023-08-08-1500-1630/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230808T103000
DTEND;TZID=Asia/Seoul:20230808T120000
DTSTAMP:20231212T062851
CREATED:20230720T004506Z
LAST-MODIFIED:20230720T004633Z
UID:2375-1691490600-1691496000@ccg.ibs.re.kr
SUMMARY:Kyeong-Dong Park\, K-stability of Fano Spherical Varieties\, II
DESCRIPTION: Speaker\n\n\nKyeong-Dong Park\nGyeongsang National University\n\n\n\n\n\n\nThe aim of this seminar is to provide participants with a comprehensive understanding of the paper “K-stability of Fano spherical varieties” by Thibaut Delcroix. For a reductive algebraic group G\, a normal G-variety is called spherical if it contains an open B-orbit\, where B is a fixed Borel subgroup of G. The class of spherical varieties contains several important families which were studied independently\, for example\, toric varieties\, rational homogeneous varieties\, group embeddings\, horospherical varieties\, symmetric varieties\, and wonderful varieties. They are classified by combinatorial objects called colored fans\, which generalize the fans appearing in the classification of toric varieties. We discuss Delcroix’s combinatorial criterion for K-stability of a smooth Fano spherical variety in terms of the barycenter of its moment polytope with respect to the Duistermaat-Heckman measure and data associated to the corresponding spherical homogeneous space. \n(1) Spherical varieties\, colored fans\, and algebraic moment polytopes \n(2) Criterion for K-stability of Fano spherical varieties and its applications \n(3) Equivariant test configurations with horospherical central fiber\, and modified Futaki invariant
URL:https://ccg.ibs.re.kr/event/2023-08-08-1030-1200/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230807T150000
DTEND;TZID=Asia/Seoul:20230807T163000
DTSTAMP:20231212T062851
CREATED:20230720T004336Z
LAST-MODIFIED:20230802T043609Z
UID:2372-1691420400-1691425800@ccg.ibs.re.kr
SUMMARY:Kyeong-Dong Park\, K-stability of Fano Spherical Varieties\, I
DESCRIPTION: Speaker\n\n\nKyeong-Dong Park\nGyeongsang National University\n\n\n\n\n\n\nThe aim of this seminar is to provide participants with a comprehensive understanding of the paper “K-stability of Fano spherical varieties” by Thibaut Delcroix. For a reductive algebraic group G\, a normal G-variety is called spherical if it contains an open B-orbit\, where B is a fixed Borel subgroup of G. The class of spherical varieties contains several important families which were studied independently\, for example\, toric varieties\, rational homogeneous varieties\, group embeddings\, horospherical varieties\, symmetric varieties\, and wonderful varieties. They are classified by combinatorial objects called colored fans\, which generalize the fans appearing in the classification of toric varieties. We discuss Delcroix’s combinatorial criterion for K-stability of a smooth Fano spherical variety in terms of the barycenter of its moment polytope with respect to the Duistermaat-Heckman measure and data associated to the corresponding spherical homogeneous space. \n(1) Spherical varieties\, colored fans\, and algebraic moment polytopes \n(2) Criterion for K-stability of Fano spherical varieties and its applications \n(3) Equivariant test configurations with horospherical central fiber\, and modified Futaki invariant
URL:https://ccg.ibs.re.kr/event/2023-08-07-1500-1630/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230807T140000
DTEND;TZID=Asia/Seoul:20230807T145000
DTSTAMP:20231212T062851
CREATED:20230802T061117Z
LAST-MODIFIED:20230802T061320Z
UID:2425-1691416800-1691419800@ccg.ibs.re.kr
SUMMARY:Minseong Kwon\, Spherical Geometry of Hilbert Schemes of Conics in Adjoint Varieties
DESCRIPTION: Speaker\n\n\nMinseong Kwon\nKAIST\n\n\n\n\n\n\nFor each rational homogeneous space\, the space of lines is now well-understood and can be described in terms of the induced group action. It is natural to consider rational curves of higher degree\, and in this talk\, we discuss geometry of conics in adjoint varieties\, which are rational homogeneous spaces associated to simple Lie algebras. Each adjoint variety is equipped with a hyperplane distribution called the contact distribution\, and we show that smooth conics transverse to the contact distribution form a homogeneous symmetric variety if the adjoint variety is of Picard number 1. This enables us to view the Hilbert scheme of conics as a spherical variety\, and we compute its colored fan by using the description of the space of lines and the Hilbert-Chow morphism.
URL:https://ccg.ibs.re.kr/event/2023-08-07-1400-1450/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230725T110000
DTEND;TZID=Asia/Seoul:20230725T120000
DTSTAMP:20231212T062851
CREATED:20230712T131020Z
LAST-MODIFIED:20230716T052748Z
UID:2356-1690282800-1690286400@ccg.ibs.re.kr
SUMMARY:Patrick Brosnan\, How Markman Saves the Hodge Conjecture (for Weil Type Abelian Fourfolds) from Kontsevich\, II
DESCRIPTION: Speaker\n\n\nPatrick Brosnan\nUniversity of Maryland\n\n\n\n\n\n\nI’ll explain what I know about two very interesting pieces of work: \n(1) Markman’s proof of the Hodge conjecture for Weil type abelian fourfolds of discriminant 1. \n(2) Kontsevich’s tropical approach to looking for counterexamples to the Hodge conjecture for Weil type abelian varieties. \nThen I’ll explain a simple observation of mine\, which implies that Kontsevich’s approach cannot work for abelian fourfolds of any discriminant. \nI’ll start out by explaining the statement of (1) precisely along with the geometric input that is required in (2). Then I’ll formulate my observation\, which is really about why the discriminant determines what types of degenerations an abelian fourfold of Weil type can have. Along the way\, I’ll take the opportunity to say a little bit about Markman’s proof of (1).
URL:https://ccg.ibs.re.kr/event/2023-07-25-1100-1200/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230720T110000
DTEND;TZID=Asia/Seoul:20230720T120000
DTSTAMP:20231212T062851
CREATED:20230712T130908Z
LAST-MODIFIED:20230716T052735Z
UID:2354-1689850800-1689854400@ccg.ibs.re.kr
SUMMARY:Patrick Brosnan\, How Markman Saves the Hodge Conjecture (for Weil Type Abelian Fourfolds) from Kontsevich\, I
DESCRIPTION: Speaker\n\n\nPatrick Brosnan\nUniversity of Maryland\n\n\n\n\n\n\nI’ll explain what I know about two very interesting pieces of work: \n(1) Markman’s proof of the Hodge conjecture for Weil type abelian fourfolds of discriminant 1. \n(2) Kontsevich’s tropical approach to looking for counterexamples to the Hodge conjecture for Weil type abelian varieties. \nThen I’ll explain a simple observation of mine\, which implies that Kontsevich’s approach cannot work for abelian fourfolds of any discriminant. \nI’ll start out by explaining the statement of (1) precisely along with the geometric input that is required in (2). Then I’ll formulate my observation\, which is really about why the discriminant determines what types of degenerations an abelian fourfold of Weil type can have. Along the way\, I’ll take the opportunity to say a little bit about Markman’s proof of (1).
URL:https://ccg.ibs.re.kr/event/2023-07-20/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230711T160000
DTEND;TZID=Asia/Seoul:20230711T170000
DTSTAMP:20231212T062851
CREATED:20230621T041523Z
LAST-MODIFIED:20230621T041523Z
UID:2343-1689091200-1689094800@ccg.ibs.re.kr
SUMMARY:Qifeng Li\, Rigidity of Projective Symmetric Manifolds of Picard Number 1 Associated to Composition Algebras
DESCRIPTION: Speaker\n\n\nQifeng Li\nShandong University\n\n\n\n\n\n\nTo each complex composition algebra A\, there associates a projective symmetric manifold X(A) of Picard number 1. The vareity X(A) is closed related with Freudenthal’s Magic Square\, which is a square starting from the adjiont varieties of F4\, E6\, E7 and E8. In a recent joint work with Yifei Chen and Baohua Fu\, we obtain the deformation rigidity of X(A). In this talk\, we will introduce the construction of X(A) from Freudenthal’s Magic Square\, the geometric properties of them\, and finally the deformation rigidity of X(A).
URL:https://ccg.ibs.re.kr/event/2023-07-11/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230622T110000
DTEND;TZID=Asia/Seoul:20230622T120000
DTSTAMP:20231212T062851
CREATED:20230310T045150Z
LAST-MODIFIED:20230601T124014Z
UID:2130-1687431600-1687435200@ccg.ibs.re.kr
SUMMARY:Shin-Young Kim\, Minimal Rational Curves on Complete Symmetric Varieties
DESCRIPTION: Speaker\n\n\nShin-Young Kim\nIBS-CGP\n\n\n\n\n\n\nWe describe the families of minimal rational curves on any complete symmetric variety\, and the corresponding varieties of minimal rational tangents. In particular\, we prove that these varieties are homogeneous and that for non-exceptional irreducible wonderful varieties\, there is a unique family of minimal rational curves. We relate these results to the restricted root system of the associated symmetric space. In particular\, for certain Fano wonderful symmetric varieties\, the VMRT has two connected components. This is a joint work with M.Brion and N. Perrin.
URL:https://ccg.ibs.re.kr/event/2023-06-22/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230616T153000
DTEND;TZID=Asia/Seoul:20230616T170000
DTSTAMP:20231212T062851
CREATED:20230510T091234Z
LAST-MODIFIED:20230510T091234Z
UID:2291-1686929400-1686934800@ccg.ibs.re.kr
SUMMARY:Minseong Kwon\, Introduction to Grauert Tubes
DESCRIPTION: Speaker\n\n\nMinseong Kwon\nKAIST\n\n\n\n\n\n\nTBA
URL:https://ccg.ibs.re.kr/event/2023-06-16/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230614T153000
DTEND;TZID=Asia/Seoul:20230614T170000
DTSTAMP:20231212T062851
CREATED:20230510T091121Z
LAST-MODIFIED:20230510T091121Z
UID:2289-1686756600-1686762000@ccg.ibs.re.kr
SUMMARY:Paul-Andi Nagy\, Introduction to Feix-Kaledin Construction
DESCRIPTION: Speaker\n\n\nPaul-Andi Nagy\nIBS-CCG\n\n\n\n\n\n\nTBA
URL:https://ccg.ibs.re.kr/event/2023-06-14/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230406T110000
DTEND;TZID=Asia/Seoul:20230406T120000
DTSTAMP:20231212T062851
CREATED:20230310T045023Z
LAST-MODIFIED:20230327T014355Z
UID:2128-1680778800-1680782400@ccg.ibs.re.kr
SUMMARY:Donggun Lee\, Birational Geometry of Generalized Hessenberg Varieties and the Generalized Shareshian-Wachs Conjecture
DESCRIPTION: Speaker\n\n\nDonggun Lee\nIBS-CCG\n\n\n\n\n\n\nHessenberg varieties are subvarieties of flag varieties with interesting properties in both algebro-geometric and combinatorial perspectives. The Shareshian-Wachs conjecture connects their cohomology with the chromatic quasi-symmetric functions of the associated graphs\, which are refinements of the chromatic polynomials. In this talk\, we introduce generalized Hessenberg varieties and study their birational geometry via blowups. As a result\, natural maps from Hessenberg varieties to projective spaces or the permutohedral varieties are decomposed into explicit blowups and projective bundle maps. As a byproduct\, we also provide an elementary proof of the Shareshian-Wachs conjecture and its natural generalization. This is joint work with Prof. Young-Hoon Kiem.
URL:https://ccg.ibs.re.kr/event/2023-04-06/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230330T110000
DTEND;TZID=Asia/Seoul:20230330T120000
DTSTAMP:20231212T062851
CREATED:20230214T085114Z
LAST-MODIFIED:20230306T010918Z
UID:2086-1680174000-1680177600@ccg.ibs.re.kr
SUMMARY:Insong Choe\, Subsheaves of Maximal Rank in a Symplectic and Orthogonal Bundle over a Curve
DESCRIPTION: Speaker\n\n\nInsong Choe\nKunkuk University\n\n\n\n\n\n\nWe first review the known results on the Quot schemes on a smooth algebraic curve. Next we explain how they can be generalized to the Lagrangian Quot scheme\, which parametrizes Lagrangian subsheaves on a symplectic vector bundle. Also we discuss the parallel results for orthogonal bundles. This will be an overview of the findings over the past 15 years in collaboration with George H. Hitching and D. Cheong.
URL:https://ccg.ibs.re.kr/event/2023-03-30/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230309T110000
DTEND;TZID=Asia/Seoul:20230309T120000
DTSTAMP:20231212T062851
CREATED:20230214T024155Z
LAST-MODIFIED:20230214T024155Z
UID:2083-1678359600-1678363200@ccg.ibs.re.kr
SUMMARY:Donghoon Jang\, Circle Actions on Almost Complex Manifolds with Isolated Fixed Points
DESCRIPTION: Speaker\n\n\nDonghoon Jang\nPusan National University\n\n\n\n\n\n\nWe briefly review group actions on manifolds and equivariant cohomology\, which is cohomology of a manifold with a group action. We review classification results for circle actions on various types of manifolds in low dimensions. An almost complex manifold is a manifold with a complex structure on its tangent bundle; every complex or symplectic manifold is almost complex. For an action of the circle group on a compact almost complex manifold that has isolated fixed points\, we study its properties and discuss the classification when the number of fixed points is small.
URL:https://ccg.ibs.re.kr/event/2023-03-09/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230302T110000
DTEND;TZID=Asia/Seoul:20230302T120000
DTSTAMP:20231212T062851
CREATED:20230214T023938Z
LAST-MODIFIED:20230214T023938Z
UID:2081-1677754800-1677758400@ccg.ibs.re.kr
SUMMARY:Yunhyung Cho\, Monotone Lagrangian Tori in Fano Varieties
DESCRIPTION: Speaker\n\n\nYunhyung Cho\nSungkyunkwan University\n\n\n\n\n\n\nThis is a survey talk of current progress of mirror symmetry of Fano varieties. For a given smooth Fano variety X\, it has been conjectured that there exists a Laurent polynomial called a (weak) Landau-Ginzburg mirror (or weak LG mirror shortly) which encodes a quantum cohomology ring structure of X. Tonkonog proved that one can find a weak LG mirror using a monotone Lagrangian torus in X. In this talk I will explain how to find a monotone Lagrangian torus using a Fano toric degeneration of X. If time permits\, I will also describe a monotone Lagrangian torus in a given flag variety.
URL:https://ccg.ibs.re.kr/event/2023-03-02/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230209T110000
DTEND;TZID=Asia/Seoul:20230209T120000
DTSTAMP:20231212T062851
CREATED:20230111T041445Z
LAST-MODIFIED:20230111T041455Z
UID:1998-1675940400-1675944000@ccg.ibs.re.kr
SUMMARY:Laurent Stolovitch\, Introduction to Normal Form Theory of Holomorphic Vector Fields 2
DESCRIPTION: Speaker\n\n\nLaurent Stolovitch\nUniversite Cote d’Azur\n\n\n\n\n\n\nIn this short lecture\, I will introduce the notion of normal form and resonances. I will also explain the phenomenon of “small divisors” and give some fundamental results of holomorphic conjugacy to a normal form.
URL:https://ccg.ibs.re.kr/event/2023-02-09/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230207T160000
DTEND;TZID=Asia/Seoul:20230207T170000
DTSTAMP:20231212T062851
CREATED:20230111T041331Z
LAST-MODIFIED:20230111T041331Z
UID:1996-1675785600-1675789200@ccg.ibs.re.kr
SUMMARY:Laurent Stolovitch\, Introduction to Normal Form Theory of Holomorphic Vector Fields 1
DESCRIPTION: Speaker\n\n\nLaurent Stolovitch\nUniversite Cote d’Azur\n\n\n\n\n\n\nIn this short lecture\, I will introduce the notion of normal form and resonances. I will also explain the phenomenon of “small divisors” and give some fundamental results of holomorphic conjugacy to a normal form.
URL:https://ccg.ibs.re.kr/event/2023-02-07/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20230202T160000
DTEND;TZID=Asia/Seoul:20230202T170000
DTSTAMP:20231212T062851
CREATED:20221222T052415Z
LAST-MODIFIED:20221222T052415Z
UID:1936-1675353600-1675357200@ccg.ibs.re.kr
SUMMARY:Dennis The\, A Cartan-theoretic Perspective on (2\,3\,5)-distributions
DESCRIPTION: Speaker\n\n\nDennis The\nUiT The Arctic University of Norway\n\n\n\n\n\n\nGeneric rank 2 distributions on 5-manifolds\, i.e. “(2\,3\,5)-distributions”\, are interesting geometric structures arising in the study of non-holonomic systems\, underdetermined ODE of Monge type\, conformal 5-manifolds with special holonomy\, etc. The origins of their study date to Élie Cartan’s “5-variables” paper of 1910\, where he gave a tour-de-force application of his method of equivalence. In my talk\, I’ll revisit the classification of homogeneous (2\,3\,5)-distributions from a modern “Cartan-theoretic” perspective. In particular\, I’ll discuss from this viewpoint the exceptionality of the 3:1 ratio for two spheres rolling on each other without twisting or slipping.
URL:https://ccg.ibs.re.kr/event/2023-02-02/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20221027T110000
DTEND;TZID=Asia/Seoul:20221027T120000
DTSTAMP:20231212T062851
CREATED:20220907T075418Z
LAST-MODIFIED:20221011T102020Z
UID:1701-1666868400-1666872000@ccg.ibs.re.kr
SUMMARY:Jaewoo Jeong\, Hankel Index of Smooth Non-ACM Curves of Almost Minimal Degree
DESCRIPTION: Speaker\n\n\nJaewoo Jeong IBS CCG\n\n\n\n\n \nThe Hankel index of a real variety is a semi-algebraic invariant that quantifies the (structural) difference between nonnegative quadrics and sums of squares on the variety. Note that the Hankel index of a variety is difficult to compute and was computed for just few cases. In 2017\, Blekherman\, Sinn\, and Velasco provided an captivating (lower) bound of the Hankel index of a variety by an algebraic invariant\, Green-Lazarsfeld index\, of the variety. In particular\, if the variety X is an arithmetrically Cohen-Macaulay (ACM) variety of almost minimal degree\, then the Hankel index of X equals to the Green-Lazarsfeld index of X plus one (which is the equality case of the bound). We study the Hankel index of smooth non-ACM curves of almost minimal degree. Note that the curve is the image of the projection of rational normal curves away from an outer point. It is known that the Green-Lazarsfeld index of the curve is determined by the rank of the center of the projection with respect to the rational normal curve. We found a new rank of the center that detects the Hankel index of the rational curves. In addition\, it turns out that the rational curves are the first class of examples that the lower bound of the Hankel index is strict.
URL:https://ccg.ibs.re.kr/event/2022-10-27/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20221013T110000
DTEND;TZID=Asia/Seoul:20221013T120000
DTSTAMP:20231212T062851
CREATED:20220830T070032Z
LAST-MODIFIED:20220928T015047Z
UID:1693-1665658800-1665662400@ccg.ibs.re.kr
SUMMARY:Jinhyun Park\, A Reciprocity Theorem Arising from a Family of Algebraic Curves
DESCRIPTION: Speaker\n\n\nJinhyun Park\nKAIST\n\n\n\n\n\n\nThe classical reciprocity theorem\, also called the residue theorem\, states that the sum of the residues of a rational (meromorphic) differential form on a compact Riemann surface is zero. Its generalization to smooth projective curves over a field is often called the Tate reciprocity theorem. \nThere is a different “multiplicative version” too. Here\, instead of a rational form\, one uses a pair of rational functions on a smooth projective curve\, and instead of residues\, one uses “Tame symbols”. The corresponding global result is called the Weil reciprocity. This result is elegantly reformulated in terms of the Milnor K-theory\, and it is generalized to sequences of rational functions by A. Suslin. This Suslin reciprocity was recently strengthened by D. Rudenko\, resolving a conjecture of A. Goncharov. \nIn this talk\, let me sketch my recent work in-progress\, that studies a different kind of reciprocity results coming from a proper family of algebraic curves over an algebraically closed field of characteristic 0.
URL:https://ccg.ibs.re.kr/event/2022-10-13/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220915T110000
DTEND;TZID=Asia/Seoul:20220915T120000
DTSTAMP:20231212T062851
CREATED:20220822T053515Z
LAST-MODIFIED:20220828T054540Z
UID:1677-1663239600-1663243200@ccg.ibs.re.kr
SUMMARY:Benjamin McMillan\, The Range of the Killing Operator
DESCRIPTION: Speaker\n\n\nBenjamin McMillan\nIBS-CCG\n\n\n\n\n\n\nThe Killing operator in (semi) Riemannian geometry has well understood kernel: the infinitesimal symmetries of a given metric. At the next level\, the range of the Killing operator can be interpreted as those perturbations of the metric that result from a mere change of coordinates—in contexts like general relativity\, the trivial perturbations. The range of the Killing operator\, albeit important\, has not been as well understood as its kernel. I will describe how one can use the projective nature of the Killing operator to reduce the question to that of the range of a connection on an associated bundle\, and then how one can seek to understand the range of an arbitrary connection. This process yields a fairly complete answer on locally symmetric spaces. \nBased on joint work with Federico Costanza\, Mike Eastwood\, and Thomas Leistner.
URL:https://ccg.ibs.re.kr/event/2022-09-15/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220901T110000
DTEND;TZID=Asia/Seoul:20220901T120000
DTSTAMP:20231212T062851
CREATED:20220822T053338Z
LAST-MODIFIED:20220822T065042Z
UID:1673-1662030000-1662033600@ccg.ibs.re.kr
SUMMARY:Guolei Zhong\, Dynamical Characterization of Projective Toric Varieties
DESCRIPTION: Speaker\n\n\nGuolei Zhong\nIBS-CCG\n\n\n\n\n\nAs a fundamental building block of the equivariant minimal model program\, the rationally connected variety plays a significant role in the classification of projective varieties admitting non-isomorphic endomorphisms. Twenty years ago\, Nakayama confirmed Sato’s conjecture that\, a smooth projective rational surface is toric if and only if it admits a non-isomorphic endomorphism. In this talk\, I will survey some recent progress on a higher dimensional analogue of Nakayama’s result. This talk is based on some joint works with Jia Jia\, Sheng Meng and De-Qi Zhang.
URL:https://ccg.ibs.re.kr/event/2022-09-01/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220324T162000
DTEND;TZID=Asia/Seoul:20220324T172000
DTSTAMP:20231212T062851
CREATED:20220304T075827Z
LAST-MODIFIED:20220304T075827Z
UID:1197-1648138800-1648142400@ccg.ibs.re.kr
SUMMARY:Hoseob Seo\, On L2 Extension from Singular Hypersurfaces
DESCRIPTION: Speaker\n\n\nHoseob Seo\nIBS CCG\n\n\n\n\n\nIn L2 extension theorems from an irreducible singular hypersurface in a complex manifold\, important roles are played by certain measures such as the Ohsawa measure\, which determines when a given function can be extended. In this talk\, we show that the singularity of the Ohsawa measure can be identified in terms of algebraic geometry.\nUsing this\, we give an analytic proof of the inversion of adjunction in this setting. These considerations enable us to compare various positive and negative results on L2 extension from singular hypersurfaces. In particular\, we generalize a recent negative result of Guan and Li which places limitations on strengthening such L2 extension by employing a less singular measure in the place of the Ohsawa measure. This is joint work with Dano Kim.
URL:https://ccg.ibs.re.kr/event/2022-03-24-1620/
LOCATION:B234
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220324T150000
DTEND;TZID=Asia/Seoul:20220324T160000
DTSTAMP:20231212T062851
CREATED:20220324T060000Z
LAST-MODIFIED:20220314T062449Z
UID:1200-1648134000-1648137600@ccg.ibs.re.kr
SUMMARY:Yonghwa Cho\, Nodal Sextics and Even Sets of Nodes
DESCRIPTION: Speaker\n\n\nYonghwa Cho\nIBS CCG\n\n\n\n\n\nIt is a classical question to ask how many nodes may a surface contain. For sextics\, the maximum number of nodes is 65\, and is attained by Barth’s example. We ask further: are all sextics with 65 nodes like Barth’s example? To find an answer\, we study even sets of nodes on sextic surfaces\, and prove that all sextics with 65 nodes share the same structure of even sets. This establishes a resemblance between Barth’s sextic and other sextics with 65 nodes. This talk is based on a joint work with Fabrizio Catanese\, Michael Kiermaier\, and Sascha Kurz.
URL:https://ccg.ibs.re.kr/event/2022-03-24-1500/
LOCATION:B234
CATEGORIES:Complex Geometry Seminar
END:VEVENT
END:VCALENDAR