복소기하학연구단
Speaker Jihun Yum IBS, Center for Complex Geometry Let 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 DF(Ω) := supρ { 0 < η < 1 : -(-ρ)η is strictly plurisubharmonic on Ω …
Speaker Seungjae Lee IBS, Center for Complex Geometry Let 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 …
Speaker Seungjae Lee IBS, Center for Complex Geometry As 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 …
Speaker Taeyong Ahn Inha University, Department of Mathematics Education In 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 …
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 …
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 …
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 …
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 …
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 …
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 …
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.
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 …