### Activity

#### GAIA Seminar on Complex Analytic Geometry - Jihun Yum

- 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.) |

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

- 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.) |

#### GAIA Seminar on Complex Analytic Geometry - 전상학

- 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. |

#### GAIA Seminar on Complex Analytic Geometry - Ngoc Cuong Nguyen

- 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.) |

#### GAIA Seminar on Complex Analytic Geometry - Ngoc Cuong Nguyen

- 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.) |

#### GAIA Seminar on Complex Analytic Geometry - Seungro Joo

- 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.) |

#### GAIA Seminar on Complex Analytic Geometry - Jihun Yum

- 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.) |

#### GAIA 수학사 강연

연사: 김영욱 교수 (고려대학교, 한국수학사학회 회장)
제목: 우리
옛 수학은 어떠했는가?
시간:
장소: 수리과학관 404호 Poster <--click |

#### GAIA Seminar on Complex Analytic Geometry - Hanjin Lee

- 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.) |

#### GAIA Seminar on Complex Analytic Geometry - Ngoc Cuong Nguyen

- 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.) |

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