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 
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 
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. 
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. 
 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 
 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 
 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

 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

 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 
 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 
 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.) 
 Title:Lpregularity
problem on general Hartogs triangles
 Speaker: Dr. Inyoung Park (GAIA)  Abstract: In
this talk, I study the Lp 
boundedness of the Bergman projection on thin and fat Hartogs triangles given
by Edholm and Mcneal [1], [2] and I will introduce some related problems.
References  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Variation of the moduli disk
for an open Riemann surface of finite genus  Speaker: Prof. Sachiko Hamano (Osaka City University, Japan)
 Abstract:
For an open Riemann surface R of finite genus, we shall consider conformal embeddings of R into closed ones of the same genus. The closing induces the Riemann's period matrix T. Masakazu Shiba and Hiroshi Yamaguchi recently showed that each diagonal element of T describes a close disk M in the upper half plane. In this talk, we shall consider the deforming open Riemann surface R(t) of finite genus with complex parameter t, and show the close relation between pseudoconvexity and the closed disk M(t) for R(t). This talk is based on a joint work with H.Yamaguchi.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Estimates of squeezing function of Thullen domain at
the origin  Speaker: Sejun Kim (POSTECH Graduate student)  Abstract: In the paper of DengGuanZhang, they
showed that there exists onetoone function from bounded domain to unit ball
which realizes squeezing function value. But for arbitrary bounded domain,
founding the squeezing function value and the realizing function is very hard.
In this talk, I will talk how to estimate of squeezing function of Thullen
domain at the origin.
 Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Stein manifolds M for which O (M) is isomorphic as Fréchet spaces,to power series spaces  Speaker: Prof. Aydin Aytuna (Sabanci University)  Details Ⅰ. Nuclear Fréchet Spaces 16:0018:00 on Tuesday, 18 April 2017 Ⅱ. Stein manifolds M for which O(M) is isomorphic to O(∆^d) 16:0018:00 on Thursday, 20 April 2017 Ⅲ. Stein manifolds M for which O(M) is isomorphic to O(C^d) 20:0022:00 on Monday, 24 April 2017 Ⅳ. Linear continuous extension operators for analytic functions defi
ned on certain closed complex submanifolds V of a Stein manifold 16:0018:00 on Thursday, 27 April 2017  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: A Kobayashi pseudodistance for holomorphic bracket generating distributions  Speaker: Dr. AeRyeong Seo (KIAS)  Abstract: In this talk, I will generalize the Kobayashi pseudodistance to complex manifolds which admit holomorphic bracket generating distributions. The generalization is based on Chow's theorem in subRiemannian geometry. For a complex homogeneous manifold with an invariant holomorphic bracket generating distribution, the universal covering of $M$ is a canonical flag domain under certain condition.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Variations of KahlerEinstein metrics on bounded pseudoconvex domains  Speaker: Sungmin Yoo (POSTECH Graduate student)  Abstract: In this talk, I will talk about the results on the papers by YoungJun Choi. The main result is (strictly) plurisubharmonicity of a family of KahlerEinstein metrics on bounded (strongly) pseudoconvex domains in C^n.  Place: GAIA Seminar Room (#106, Math Science bldg.) 

 Title:
On the existence of a complete Kahler metric on noncompact complex manifolds  Speaker: Dr. Ngoc Cuong Nguyen (GAIA)  Abstract: We present the results based on the paper by Cheng and Yau. The main result is the existence of a KahlerEinstein metric on a strictly pseudoconvex bounded domain. This is proved via solving the appropriate complex MongeAmpere equation.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Lagrangian Pluripotential Theory and a Lagrange Equation of MongeAmpère Type  Speaker: Prof. H. Blaine Lawson (StonyBrook University, New York, U.S.A.)  Place: #404, Math Science bldg. POSTECH. 
 Title: Invariance of the DiederichFornaess index under CRdiffeomorphism  Speaker: Jihun
Yum (POSTECH Graduate student)
 Abstract: This is a consecutive talk of my previous talk on October 17. We will complete the following theorem : Let M1, M2 be Stein manifolds with dimension n >= 2. Let D1, D2 be relatively compact domains in M1, M2 with connected C^k (k >= 2) smooth boundaries. If the boundary of D1 and D2 are CRdiffeomorphic, then the DiederichFornaess indices of D1 and D2 are same.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: On and around the squeezing functiona survey  Speaker: Prof. KangTae Kim(POSTECH/ GAIA)  Abstract: The concept of squeezing function has been one of the hot new themes of research in these days. It came out of the geometric condition for the partial differential equations (by Cheng and Yau in the late 1980s) and became formalized by others very recently (2004, 2005, 2008, 2016...). We in GAIA as well as colleague(s) in Wuppertal have produced some and now it is catching a "fire" in the hands of Fornaess, Diederich, Wold and others in Europe. At this stage, I would like to give an overview, possibly with some good problems towards our research. This talk should be understandable to graduate students who understand basics of differential geometry and complex analysis.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Honor Thesis on Classical Nevanlinna Theory  Speaker: 전상학 (POSTECH Undergraduate student)  Abstract: He has learned this topic throughout the semester and now he presents the result of his study as part of the oral defense. He shall introduce the outline of the Nevanlinna theory that concerns the equation f(z)=c for the generic complex values for c where f is a complex analytic function of a single variable z. Along the way he shall discuss variations and further developments beyond the most basic theorems. Seminar will be presented in Korean. (Written by K.T. Kim, the advisor of this thesis work).  Place: #404, Math Science bldg. 
 Title: Weak solutions of complex Hessian equations on compact Hermitian manifolds  Speaker: Dr. Ngoc Cuong Nguyen (GAIA)  Abstract: This is a joint work with Slawomir Kolodziej. We prove the existence of weak solutions of complex mHessian equations on compact Hermitian manifolds for the nonnegative right hand side belonging to L^p, with p>n/m, (n is the dimension of the manifold). For smooth, positive data the equation has been recently solved by Szekelyhidi and Zhang. We also give a stability result for such solutions.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Dirichlet
Problem for the complex Hessian equations on a Hermitian manifold
 Speaker: Dr. Ngoc Cuong Nguyen (GAIA)  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: On a problem of J. E. Fornaess  Speaker: Seungro Joo (POSTECH Graduate student)  Abstract:The squeezing function, which has various applications, is one of invariants under biholomorphic coordinate changes. For this function, Professor J. E. Fornaess proposes the following question. Q. Let $Omega$ be a bounded pseudoconvex domain with a smooth boundary. If the squeezing function S(z) > 1 as z > p for some boundary point p of $Omega$, then is p a strongly pseudoconvex point? In this talk, we answer the question, using a scaling method, for bounded pseudoconvex domains in C^2 with a smooth finite type boundary.  Place: GAIA Seminar Room (#106, Math Science bldg.) 