 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.) 
 Title: Invariance of the DiederichFornaess index under
CRdiffeomorphism  Speaker: Jihun Yum (POSTECH Graduate student)
 Abstract:We
will first introduce about the DiederichFornaess index, and known results
related to it. And then we will consider the following question: Let M1. M2 be
complex manifolds and D1, D2 be relatively compact domains in M1, M2,
respectively. If the boundary of D1 and D2 are CRdiffeomorphic, then are the
DiederichFornaess indices of D1 and D2 same?  Place: GAIA Seminar Room (#106, Math Science bldg.) 
연사: 김영욱 교수 (고려대학교, 한국수학사학회 회장)
제목: 우리
옛 수학은 어떠했는가?
시간: 10월 13일 목요일 오후 4:305:30
장소: 수리과학관 404호 Poster <click

 Title:
Analyticity of isometries of
CR invariant metrics
 Speaker: Prof. Hanjin Lee (Hadong Global University)
 Abstract: Holomorphicity of isometries of Bergman metrics and Kobayashi
metrics on pseudoconvex domains have been studied by several people. In this
talk, CR analog of this problem will be considered. In particular, isometries
of Webster metrics and Fefferman metrics on strictly pseudoconvex CR manifolds
will be considered.
 Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Symmetrization of plurisubharmonic functions  Speaker: Dr. Ngoc Cuong Nguyen (GAIA)  Abstract: We will present a result of Berman and Berndtsson on the Schwarz symmetrization of plurisub harmonic functions. If the psh function is S^1 invariant, then the symmetrisation does not increase the MongeAmpere energy. As a consequence, one can derive the Moser Trudinger inequality for such a function.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: On Leviflat surfaces with the given boundary  Speaker: Prof. Nikolay Shcherbina (Bergische Universität Wuppertal)  Abstract: We give an overview of known results and open questions in the problem of existence and uniqueness of Leviflat surfaces with the given boundary. Special emphasis will be made on the graph case.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Tilings and unfoldings  Speaker: Prof. Stefan Langerman (University of Liver de Bruxelles)  Abstract: A tiling is a covering of the plane with copies of a geometric shape(tiles) without gaps or overlaps. An unfolding is obtained by cutting along the surface of a polyhedron through all its vetices, and opening all the digedral angles between adjacent faces to obtain a single flat nonoverlapping geometric shape. In this handson talk, I will explore connections between these two fascinating concepts, in an attempt to shed some light on the following still unsolved algorithmic problem: How easy(or hard) is it to determine if a given geometric shape can tile the plane? and the following more artistic and no less fundamental problem: How to create beautiful (or even ugly) tilings?  Place: TaeJoon Park Digital Library #502  Date: 16:0017:00 on Wednesday, 28 September 2016 
 Title: On the qBremermannDirichlet problem and polynomial convexity for unbounded sets  Speaker: Dr. Thomas Pawlaschyk (Universität Wuppertal)  Abstract: Part 1: Let D be an unbounded domain in C^n and let f be a bounded continuous function on the boundary bD of D. I show that under some (strong) conditions on D we can find a unique continuous extension F of f into D which is qplurisubharmonic, (nq1)plurisuperharmonic and which is maximal in the following sense: each qplurisubharmonic function g on D with g <= f on bD satisfies g <= F on D. Part 2: I present recent results on polynomial convexity for unbounded closed sets and the relation to approximation of holomorphic functions defined on polynomially convex sets by entire ones.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Analytic techniques in algebraic geometry  Speaker: Professor Shinichi Matsumura (Tohoku University)  Abstract: In this talk, I would like to explain fundamental facts on singular Hermitian metrics and its applications to (complex) algebraic geometry. The main topic of this talk is a generalization of the Kodaira embedding theorem to big line bundles by the L^2method for the dbar equation. Furthermore, I will explain the nonample locus of big line bundles. If time permits, I will explain the proof of the invariance of plurigenera by the OhsawaTakegoshi L^2 extension theorem.  Place: GAIA Seminar Room (#106, Math Science bldg.)  Date: Lectures 1 & 2: 810 p.m. Monday, Sept 5th, 2016 Lectures 3 & 4: 810 p.m. Thursday, Sept 8th, 2016 Poster < click 
 Title: Introduction to AndersenLempert theory  Speaker: Prof. Rafael Andrist (Bergische Universität Wuppertal)  Abstract: AndersenLempert theory deals with Rungetype approximation of holomorphic automorphisms of complexeuclidean space, and can be generalized to other Stein manifolds with a large automorphism group. It allows for a rather precise description of the group of holomorphic automorphisms of such manifolds and enables to carry out a lot of geometric constructions. We will develop the basics of AndersenLempert theory and consider some applications and geometric implications.  Place: GAIA Seminar Room (#106, Math Science bldg.)  Date: Lecture 1 : 8  10 p.m. on Tuesday, Sept 6, 2016 Lecture 2 : 4  6 p.m. on Friday, Sept 9, 2016 
 Title:Asymptotic analysis of oscillatory integrals with smooth phases and weights  Speaker: Professor Toshihiro Nose (Fukuoka Institute of Technology)  Abstract: In this talk, we study asymptotic behavior of oscillatory integrals at infinity. In real analytic phases case, A. N. Varchenko precisely investigates the leading term of the asymptotic expansion of an oscillatory integral via the Newton polyhedron of the phase under some nondegeneracy condition. We generalize and improve his result. We are especially interested in the cases that the phase is smooth and that the amplitude has a zero at a critical point of the phase. This work is joint with J. Kamimoto.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Extension of biholomorphisms between convex domains  Speaker: Prof. Hervé Gaussier (Université de GrenobleAlpes)  Abstract: This is a joint work with Filippo Bracci. The aim of the talk will be to present some extension result for univalent maps of the unit ball, or more generally of a strongly pseudoconvex domain, whose image is bounded and convex. We will prove the following Theorem. Let D be a smooth bounded strongly convex domain. Let F be a biholomorphism from D to a bounded convex domain. Then F extends as a homeomorphism.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Discreteness of subgroups of complex hyperbolic isometries
 Speaker: Dr. Lijie Sun (Tokyo Institute of Technology, Japan)
 Abstract: In this talk, we will firstly investigate the discreteness of twogenerator subgroups by characterizing Dirichlet domains and Ford domains of regular elliptic, or loxodromic, generator cyclic groups. After that, we will concentrate on the discreteness of complex hyperbolic triangle groups of type, which will be parametrized by angular invariant . We will give three explicit nondiscrete conditions in the form of and could get more explicit conclusions about thetriangle groups of type . At last, Poincaré's polyhedron theorem as vital important tool to verify the discreteness of a subgroup will be considered. We will see a particular form originally proposed by Mostow and apply it to investigation of the discrete and faithful representations of complex hyperbolic triangle groups. 
Place: GAIA Seminar Room (#106, Math Science bldg.)


 Title: Richberg's smoothing procedure
for continuous strictly plurisubharmonic functions  Speaker: Dr. Tobias Harz (GAIA)  Abstract: I
will explain a classical result on smoothing of continuous strictly plurisubharmonic
functions due to R. Richberg. In particular, I will show the following: Let
$\Omega \subset \mathbb{C}^n$ be a domain and let $\varphi: \Omega \to \mathbb{R}$
be continuous and strictly plurisubharmonic. Then for every function $\lambda: \Omega
\to (0,\infty)$ there exists a $\mathcal{C}^\infty$smooth strictly plurisubharmonic
function $\tilde{\varphi} : \Omega \to \mathbb{R}$ such that $\varphi <
\tilde{\varphi} < \varphi + \lambda$.
 Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: On the tangential holomorphic vector fields vanishing
at an infinite type point  Speaker: Sejun Kim (POSTECH Graduate student)  Abstract: R.E.
Greene and S.G. Krantz conjectured that there would not exist any noncompact
sequence of holomorphic automorphisms of a pseudoconvex domain which accumulate
to a boundary point of infinite type in the sense of DAngelo, if
the domain has smooth boundary.
It is also reasonable to consider a local version of the GreeneKrantz conjecture: Let M be a real hypersurface in C^{n} and let p ∈M. Suppose that p is a nonLeviflat point of infinite type. If X= is a holomorphic tangential vector field vanishing at p, then X is rotation. I want to find a new method of the above conjecture, in the example .  Place: GAIA Seminar Room (#106, Math Science bldg.)  Date: 8 p.m.  10 p.m on Monday, 23 May 2016 Poster < click 
 Title: Hörmander's L^{2} existence theorem(final)  Speaker: Prof. KangTae Kim(POSTECH, GAIA)  Abstract: 1. Computation/ Estimate
2. Approximation  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Hörmander's
L^{2} existence theorem, I  Speaker: Prof. KangTae Kim(POSTECH, GAIA)  Abstract: This is a continuation of my
lecture on Several Complex Variables. The contents are * The proof of formal existence theorem * The closure of dbar operator(s) * Hormander's estimates Then I shall end with the
remarks on what more should be done to complete the proof of the Levi problem,
as far as this PDE point of view is concerned.  Place: GAIA Seminar Room (#106, Math Science bldg.) 
 Title: Composition operators
between the large Bergman spaces
 Speaker: Dr. Inyoung Park (GAIA)  Abstract: I
will introduce the weighted composition operators acting on Bergman spaces with
the exponential weights. Especially, we study when a weighted composition
operator is bounded or compact. We give some characterizations on such basic
questions in terms of a symbol map inducing a composition operator. This work
is a little extension of the previous work done by T. L. Kriete and B. D.
Maccluer.
 Place: GAIA Seminar Room (#106, Math Science bldg.) 