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Several Complex Variables Seminar
Nguyen Ngoc Cuong, Hölder Continuous Solutions to Complex Monge-Ampère Equations and its Applications
B266 IBS, Korea, Republic ofJihun Yum, Classification of Domains that Admit the Bergman-Einstein Metric I
B266 IBS, Korea, Republic ofSpeaker Jihun Yum IBS, Center for Complex Geometry
Jihun Yum, Classification of Domains that Admit the Bergman-Einstein Metric II
B266 IBS, Korea, Republic ofSpeaker Jihun Yum IBS, Center for Complex Geometry
Nguyen Ngoc Cuong, Hölder Continuous Solutions to Complex Monge-Ampère Equations and its Applications II
B266 IBS, Korea, Republic ofSpeaker Nguyen Ngoc Cuong KAIST The Monge-Ampère equations provide Kähler-Einstein metrics on projective manifolds with negative or zero first Chern classes thanks to the AubinYau and Yau theorems. However, most projective manifolds do not have a negative definite or trivial first Chern class. The study of the canonical metric on these manifolds leads …
Jihun Yum, Isometric Embedding of Kähler Manifolds and the Diastatic Function
B266 IBS, Korea, Republic ofSpeaker Jihun Yum IBS, Center for Complex Geometry
Sung Yeon Kim, Nonsolvability of Lewy Operator and Non-realizable CR Structures
B266 IBS, Korea, Republic ofSpeaker Sung Yeon Kim IBS, Center for Complex Geometry
Jihun Yum, Characterization of Diederich-Fornaess and Steinness Indices in Cn
B266 IBS, Korea, Republic ofSpeaker Jihun Yum IBS, Center for Complex Geometry Let 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 DF(Ω) := supρ { 0 < η < 1 : -(-ρ)η is strictly plurisubharmonic on Ω ∩ U for some …
Jihun Yum, Characterization of Diederich-Fornaess and Steinness Indices in Complex Manifolds
B266 IBS, Korea, Republic ofSpeaker 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 …
Taeyong Ahn, Positive Closed Currents and Super-potentials
B266 IBS, Korea, Republic ofSpeaker 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 …
Young-jun Choi, Existence of a Complete Holomorphic Vector Field via the Kähler-Einstein Metric
B266 IBS, Korea, Republic ofSpeaker 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 …
Hoseob Seo, On Singularities of Toric Plurisubharmonic Funcitons
B266 IBS, Korea, Republic ofSpeaker 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 …