Activity
Student Seminar on complex Analytic Geometry_Mr. Yewon Cho
On the Hartogs Analyticity Theorem
 Place: The GAIA (Mathematical Science bldg.
Room 106)  Date: 16:0018:00
on Thursday, 15 March 2018.  Speaker: Mr. Yewon Cho(POSTECH Grad Student)  Abstract This presentation concerns the
celebrated theorem of F. Hartogs on the continuity of
separatelyanalytic functions. The goal is to obtain some insights
from the proof. Poster <Click here 
GAIA Seminar on complex Analytic Geometry_Dr. Seungro Joo
On smoothly bounded domains covering finite volume manifolds
 Place: The GAIA (Mathematical Science bldg.
Room 106)  Date: 20:0022:00
on Monday, 5 March 2018.  Speaker: Dr. Seungro Joo(GAIA)
 Abstract In this talk, we study a recent
result of Andrew Zimmer. He proved that: if a bounded domain with C2 boundary
covers a manifold which has finite volume with respect to either the Bergman
volume, the KaehlerEinstein volume, or the KobayashiEisenman volume, then the
domain is biholomorphic to the unit ball.
Poster <Click here 
GAIA Seminar on complex Analytic Geometry  Prof. Nikolay Shcherbina
On the structure of the core for domain in C^{n} ^{}
 Place: The GAIA (Mathematical Science bldg. Room 106  Date: 20:00 on Tuesday, 20 February 2018.  Speaker: Prof. Nikolay Shcherbina (Bergische Universität Wuppertal) Poster <Click here 
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
