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  • Hosung Kim, The Space of Rational Curves on a General Hypersurface of Projective Space

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

         Speaker Hosung Kim IBS, Center for Complex Geometry In 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 …

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  • Young-jun Choi, Existence of a Complete Holomorphic Vector Field via the Kähler-Einstein Metric

    B266 IBS, Korea, Republic of
    Several Complex Variables Seminar

         Speaker Young-jun Choi Pusan National University A 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 …

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  • Jeong-Seop Kim, Stability of Symmetric Powers of Vector Bundles on a Curve

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

         Speaker Jeong-Seop Kim KAIST For 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 …

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  • Lucas Kaufmann, Introduction to Dynamics in Several Complex Variables

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

         Speaker Lucas Kaufmann IBS, Center for Complex Geometry The 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. Due to the fundamental differences between complex analysis …

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  • Lucas Kaufmann, Commuting Pairs of Endomorphisms

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

         Speaker Lucas Kaufmann IBS, Center for Complex Geometry The 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 …

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  • Hoseob Seo, On Singularities of Toric Plurisubharmonic Funcitons

    B266 IBS, Korea, Republic of
    Several Complex Variables Seminar

         Speaker Hoseob Seo Research Institute of Mathematics, Seoul National University In 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 …

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  • Joonyeong Won, K-stability, Kähler-Einstein Metric on Fano Varieties and Sasaki-Einstein Metric on 5-dimensional Smale Manifolds

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

         Speaker Joonyeong Won KIAS We 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.

  • Dano Kim, Canonical Bundle Formula and Degenerating Families of Volume Forms

    on-line
    Several Complex Variables Seminar

         Speaker Dano Kim Department of Mathematical Sciences, Seoul National University We 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 …

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  • Baohua Fu, Normalized Tangent Bundle, Pseudoeffective Cone and Varieties with Small Codegree

    on-line
    Complex Geometry Seminar

         Speaker Baohua Fu Chinese Academy of Science We 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 …

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  • Pak Tung Ho, Chern-Yamabe Problem

    on-line
    Several Complex Variables Seminar

         Speaker Pak Tung Ho Sogang University I 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. I will also mention other results related to the Chern-Yamabe problem.

  • Yong Hu, Noether-Severi Inequality and Equality for Irregular Threefolds of General Type

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

         Speaker Yong Hu KIAS For 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 …

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  • Sukmoon Huh, Logarithmic Sheaves on Projective Surfaces

    B266 IBS, Korea, Republic of
    Complex Geometry Seminar

         Speaker Sukmoon Huh Sungkyunkwan University A 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 …

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