Complex Geometry Seminar

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  • Patrick Brosnan, How Markman Saves the Hodge Conjecture (for Weil Type Abelian Fourfolds) from Kontsevich, I

    B236-1 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Patrick Brosnan University of Maryland I'll explain what I know about two very interesting pieces of work: (1) Markman's proof of the Hodge conjecture for Weil type abelian fourfolds of discriminant 1. (2) Kontsevich's tropical approach to looking for counterexamples to the Hodge conjecture for Weil type abelian varieties. Then I'll explain …

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  • Patrick Brosnan, How Markman Saves the Hodge Conjecture (for Weil Type Abelian Fourfolds) from Kontsevich, II

    B236-1 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Patrick Brosnan University of Maryland I'll explain what I know about two very interesting pieces of work: (1) Markman's proof of the Hodge conjecture for Weil type abelian fourfolds of discriminant 1. (2) Kontsevich's tropical approach to looking for counterexamples to the Hodge conjecture for Weil type abelian varieties. Then I'll explain …

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  • Minseong Kwon, Spherical Geometry of Hilbert Schemes of Conics in Adjoint Varieties

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Minseong Kwon KAIST For 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 …

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  • Kyeong-Dong Park, K-stability of Fano Spherical Varieties, I

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Kyeong-Dong Park Gyeongsang National University The 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 …

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  • Kyeong-Dong Park, K-stability of Fano Spherical Varieties, II

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Kyeong-Dong Park Gyeongsang National University The 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 …

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  • Kyeong-Dong Park, K-stability of Fano Spherical Varieties, III

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Kyeong-Dong Park Gyeongsang National University The 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 …

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  • George Hitching, Brill-Noether Loci on Moduli Space of Symplectic Bundles over a Curve

    B236-1 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker George Hitching Oslo Metropolitan University Let 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 …

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  • Thomas Peternell, Semipositive Tangent Bundles and Canonical Extensions

    B236-1 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Thomas Peternell University of Bayreuth Given 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, …

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  • Yum-Tong Siu, [IBS-KAIST Seminar] Differential Relations for Multiplier Ideal Sheaves in ∂ Estimates

    B236-1 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Yum-Tong Siu Harvard University For 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. In the weak-solution approach to solving the ∂​​​ …

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  • Fabrizio Catanese, [IBS-KAIST Seminar] Geometry and Dynamics of Geometric Endomorphisms of the Hesse Moduli Space of Elliptic Curves

    B236-1 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Fabrizio Catanese University of Bayreuth We 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 …

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  • Yaoxiong Wen, Generalized Quiver Mutation and PAX/PAXY Models

    B236-1 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Yaoxiong Wen KIAS During 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 …

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  • Gil Bor, Cusps of Caustics by Reflection in a Convex Billiard Table

    B236-1 IBS, Korea, Republic of
    Complex Geometry Seminar

        Speaker Gil Bor CIMAT Place 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 …

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