Activity
GAIA Seminar on complex Analytic Geometry_Mr.Jihun Yum
DiederichFornaess index and Steinness index.  Place: GAIA Seminar Room (#106, Mathematical Science bldg.)  Date: 8 p.m.  10 p.m on Monday, 22 January 2018  Speaker: Mr. Jihun Yum (POSTECH)  Abstract: Let D be a bounded pseudoconvex domain in ℂ^n with smooth boundary. DiederichFornaess index DF(D) is η1 iff for all η ∈ (0, η1), there exists a defining function ρ such that (ρ)^η is strictly plurisubharmonic on D. Steinness index S(D) is η2 iff for all η > η2, there exist a defining function ρ and a neighborhood U of ∂D such that ρ^η is strictly plurisubharmonic on (closure{D})^c ∩ U. We will see the relation between DiederichFornaess index and Steinness index on smooth Worm domains. Poster <Click here 
GAIA Seminar on complex Analytic Geometry_Prof. Andrew Zimmer
The automorphism group and limit set of a bounded domain  Place: GAIA Seminar Room (#106, Mathematical Science bldg.)  Date: 8 p.m.  10 p.m on Monday, 8 January 2018  Speaker: Prof. Andrew Zimmer (William and Mary University)
 Abstract: For certain classes of bounded domains we give a precise description of the automorphism group and its limit set in the boundary. For instance, for finite type pseudoconvex domains we prove: if the limit set contains at least two different points, then the automorphism group has finitely many components and is the almost direct product of a compact group and connected Lie group locally isomorphic to Aut (B_{k}). Further, the limit set is a smooth submanifold diffeomorphic to the sphere of dimension 2k1. For convex domains with C^{1,ε} boundary we can prove a similar result. In this talk we will describe the main ideas of the proofs and discuss some applications. 
GAIA Seminar on complex Analytic Geometry_Prof. ChongKyu Han
Complex submanifolds in real hypersurfaces  Place: GAIA Seminar Room (#106, Mathematical Science bldg.)  Date: 8 p.m.  10 p.m on Monday, 27 November 2017  Speaker: Prof. ChongKyu Han (Seoul National University)
 Abstract: I will review first the Pfaffian system technique for overdetermined PDE systems, then present some applications. An interesting feature of complex analysis of several variables is that for smoothly bounded domains in C^{n}, n ≥ 2, function theory of the domain depends on the geometry of its boundary. In particular, whether or not the boundary contains a complex subvariety often has to be determined, mainly because it is “characteristic” for the CauchyRiemann equations. I want to present my recent results in these directions. 
GAIA Seminar on complex Analytic Geometry_Dr. Ngoc Cuong Nguyen
 Title:
On the MongeAmpère boundary measure
of a bounded hyperconvex
domain ^{}  Speaker: Dr. Ngoc Coung Nguyen (GAIA)
 Abstract:
We present results in a paper by Demailly. Let Ω be a bounded
hyperconvex domain in C^{n},
i.e., it admits a negative plurisubharmonic exhaustive function. We study the
properties of the "Pluricomplex Green function" of Ω, denoted by u_{z}(ζ), which solves the MongeAmpère
equation
(dd^{c}u_{z})^{n} = 0 on Ω \ {z}, u_{z}(ζ) ~ logz  ζ near z.
We associate to u_{z} a measure μ_{z}
supporting on ∂Ω. In general, μ_{z} is supported by the set of strictly
pseudoconvex points of ∂Ω.  Place: GAIA Seminar Room (#106, Mathematical Science bldg.)
 Date: 8 p.m.  10 p.m on Monday, 20 November 2017 Poster <Click here 
GAIA Seminar on complex Analytic Geometry_Prof. KangTae Kim
 Title: Multidimensional complex analysisSurvey lecture III ^{}  Speaker: Prof. KangTae Kim (GAIA)
 Abstract: Continuing from the lectures of the 23rd of October, I shall discuss more topics such as: (6) Extension and filling, Complex geometry vs. CR geometry (7) Approximation and polynomial convexity (8) Invariant metrics and geometric theory of holomorphic mappings  Place: GAIA Seminar Room (#106, Math Science bldg.)
 Date: 8 p.m.  10 p.m on Monday, 30 October 2017 Poster <Click here 
GAIA Seminar on complex Analytic Geometry_Prof. KangTae Kim
 Title: Multidimensional complex
analysisSurvey lecture II ^{}  Speaker: Prof. KangTae Kim (GAIA)
 Abstract: Continuing from the lectures of the 16th of October, I shall discuss more topics such as: (5) Biholomorphic and proper holomorphic mappings in connection to Geometric function theory (6) Extension and filling, Complex geometry vs. CR geometry (7) Approximation and polynomial convexity (8) Invariant metrics and geometric theory of holomorphic mappings (Still, more than 5 topics are remaining in my notes...)  Place: GAIA Seminar Room (#106, Math Science bldg.)
 Date: 7 p.m.  9 p.m on Monday, 23 October 2017

GAIA Seminar on complex Analytic Geometry_Prof. KangTae Kim
 Title: Multidimensional Complex Analysis through
Geometry; an Introduction ^{}  Speaker: Prof. KangTae Kim (GAIA)
 Abstract: Historians say that Riemann, holding in his hands the manuscript by Cauchy on complex analysis, said that this is the beginning of a new Mathematics. Not only did he say so, he also did not distinguish complex analysis and geometry. But then over time, such a view was realized, analyzed and magnified by many greats including Weierstrass, Schwarz, Carathéodory, Pick, Bergman, Ahlfors, Bochner, Weil, Kodaira, Chern, Kobayashi, Wu, Greene, Griffiths, Shabat, Chirka, Yau, Siu, Fornaess, Bedford, Gunning, Kohn, and many others. Ohsawa once said (to me) that it is better to use geometry to understand Function theory (of holomorphic functions), and I strongly agreed. This interesting line of thoughts (concerning one and multidimensional complex analysis = Theory of holomorphic functions in all dimensions) may be worthy of (re)checking overall on perspective. This lecture does not aim at the level of researchers of the field of Complex Analytic Geometry and Complex Geometric Analysis. Rather, it is for the general audience (though limited, automatically).  Place: GAIA Seminar Room (#106, Math Science bldg.)
 Date: 8 p.m.  10 p.m on Monday, 16 October 2017

GAIA Seminar on complex Analytic Geometry_Dr. Ngoc Cuong Nguyen
 Title: Hölder continuous solutions of the Monge–Ampère equation on compact Hermitian manifolds^{ } ^{}  Speaker: Dr. Ngoc Cuong Nguyen (GAIA)
 Abstract: This is a joint work with S. Kolodziej. We show that a positive Borel measure of finite total mass, on compact Hermitian manifolds, admits a Hölder continuous quasiplurisubharmonic solution to the Monge Ampère equation if and only if it is dominated locally by MongeAmpere measures of Holder continuous plurisubharmonic functions.  Place: GAIA Seminar Room (#106, Math Science bldg.)
 Date: 8 p.m.  10 p.m on Monday, 25 september 2017 ^{} Poster < click 
GAIA Seminar on complex Analytic Geometry_Dr. Seungro Joo
 Title: Compactness of certain families of pseudoholomorphic mapping into C^{n}
 Speaker: Dr. Seungro Joo (POSTECH)
 Abstract: We study a concept of the convexity index, which is define in[I]. In this paper, Gaussier & Kim showed some normal family arguments for the sequence whose image has a uniform positive lower bound of the convexity index.
Reference: [I] H.Gaussier and K.T Kim, Compactness of certain families of
pseudoholomorphic mapping into C^{n}, Int.J.Math. 15(1) (2004), 112
 Place: GAIA Seminar Room (#106, Math Science bldg.)
 Date: 8 p.m.  10 p.m on Monday, 18 september 2017 ^{ }
Poster < click 
GAIA Seminar on complex Analytic Geometry_Prof. KangTae Kim
 Title: On the squeezing function for Pseudoconvex domain in C^n  Speaker: Prof. KangTae Kim(POSTECH)  Abstract: We shall present a survey of recent results on this branch of research.
** Nikolay Nikolov’s recent result will be presented in the last 30 minutes by Dr. Seungro Joo.  Place: GAIA Seminar Room (#106, Math Science bldg.) 