Activity

GAIA Seminar on Complex Analytic Geometry - Jihun Yum

posted Dec 11, 2016, 5:33 PM by Hyemin Shin   [ updated Dec 12, 2016, 4:22 PM ]

- Title: Invariance of the Diederich-Fornaess index under CR-diffeomorphism

- 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 CR-diffeomorphic, then the Diederich-Fornaess indices of D1 and D2 are same.


- Place: GAIA Seminar Room (#106, Math Science bldg.)
 
- Date: 8 p.m. - 10 p.m on Monday, 19 December 2016


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GAIA Seminar on Complex Analytic Geometry - Prof. Kang-Tae Kim

posted Dec 6, 2016, 6:52 PM by Hyemin Shin

- Title: On and around the squeezing function---a survey

- Speaker: Prof. Kang-Tae 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.)
 
- Date: 8 p.m. - 10 p.m on Monday, 12 December 2016


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GAIA Seminar on Complex Analytic Geometry - 전상학

posted Nov 24, 2016, 10:12 PM by Hyemin Shin   [ updated Dec 5, 2016, 12:30 AM ]

-  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.
 
- Date: 16:30 on Thursday, 8 December 2016
 

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GAIA Seminar on Complex Analytic Geometry - Ngoc Cuong Nguyen

posted Nov 24, 2016, 10:10 PM by Hyemin Shin

-  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 m-Hessian 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.)
 
- Date: 8 - 10 p.m. on Monday, 5 December 2016
 

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GAIA Seminar on Complex Analytic Geometry - Ngoc Cuong Nguyen

posted Nov 3, 2016, 12:15 AM by Hyemin Shin

-  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.)
 
- Date: 8 - 10 p.m. on Monday, 7 November 2016
 

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GAIA Seminar on Complex Analytic Geometry - Seungro Joo

posted Oct 17, 2016, 6:48 PM by Hyemin Shin

-  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.)
 
- Date: 5 - 6 p.m. on Thursday, 20 October, 2016
 

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GAIA Seminar on Complex Analytic Geometry - Jihun Yum

posted Oct 12, 2016, 12:56 AM by Hyemin Shin

-  Title: Invariance of the Diederich-Fornaess index under CR-diffeomorphism

-  Speaker: Jihun Yum (POSTECH Graduate student)

-  Abstract:We will first introduce about the Diederich-Fornaess 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 CR-diffeomorphic, then are the Diederich-Fornaess indices of D1 and D2 same?

- Place: GAIA Seminar Room (#106, Math Science bldg.)
 
- Date: 8 - 10 p.m. on Monday, October 17, 2016
 

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GAIA 수학사 강연

posted Oct 10, 2016, 11:05 PM by Hyemin Shin

연사: 김영욱 교수 (고려대학교, 한국수학사학회 회장)

 

제목: 우리 옛 수학은 어떠했는가?

요약: 동양도 서양처럼 나라나 백성에 필요한 수학과 과학을 연구하고 발전시켰다. 2700년 정도 전부터 이미 여러 가지 문제를 풀 줄 알았고 500년에 걸친 발전을 책으로 엮어내었으나 진시황의 분서갱유 사건으로 대부분 없어졌다. 흩어진 것을 다시 모아 책으로 만들고 발전시켜 지금 전해지는 구장산술이 생겨났다. 우리도 신라시대에 이를 받아들여 꾸준히 사용하고 발전시켰다고 보인다.
이 강의에서는 세 가지 정도를 간단히 알아본다: 첫째, 동양수학은 왜 없어지고 서양수학만 남았나? 둘째, 중국 수학은 어떻게 발전했나? 셋째, 우리는 수학을 얼마나 공부했는가?

 

 

시간: 1013일 목요일 오후 4:30-5:30

 

장소: 수리과학관 404


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GAIA Seminar on Complex Analytic Geometry - Hanjin Lee

posted Oct 6, 2016, 1:15 AM by Hyemin Shin

-  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.)
 
- Date: 8 - 10 p.m. on Monday, October 10, 2016
 

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GAIA Seminar on Complex Analytic Geometry - Ngoc Cuong Nguyen

posted Sep 18, 2016, 11:38 PM by Hyemin Shin

-  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 Monge-Ampere energy. As a consequence, one can derive the Moser- Trudinger inequality for such a function.


- Place: GAIA Seminar Room (#106, Math Science bldg.)
 
- Date: 8 - 10 p.m. on Tuesday, October 4, 2016
 

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