Activity

GAIA Seminar on complex Analytic Geometry_Mr.Jihun Yum

posted Jan 15, 2018, 5:48 PM by Eunyoung Choi   [ updated Jan 15, 2018, 5:48 PM ]

Diederich-Fornaess index and Steinness index.

- Place: GAIA Seminar Room (#106, Mathematical Science bldg.)

- Date: 8 p.m. - 10 p.m on Monday, 22 January 2018

- SpeakerMr. Jihun Yum (POSTECH)


- Abstract: 

Let D be a bounded pseudoconvex domain in ^n with smooth boundary. Diederich-Fornaess 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 Diederich-Fornaess index and Steinness index on smooth Worm domains.



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GAIA Seminar on complex Analytic Geometry_Prof. Andrew Zimmer

posted Jan 1, 2018, 4:45 PM by Eunyoung Choi   [ updated Jan 1, 2018, 8:03 PM ]

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

- SpeakerProf. 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 (Bk). Further, the limit set is a smooth submanifold diffeomorphic to the sphere of dimension 2k-1. For convex domains with C1,ε boundary we can prove a similar result. In this talk we will describe the main ideas of the proofs and discuss some applications.


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GAIA Seminar on complex Analytic Geometry_Prof. Chong-Kyu Han

posted Nov 20, 2017, 5:51 PM by Eunyoung Choi   [ updated Nov 20, 2017, 8:42 PM ]

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

- SpeakerProf. Chong-Kyu 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 Cn

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 Cauchy-Riemann equations.

I want to present my recent results in these directions.


 Poster  <---Click here


GAIA Seminar on complex Analytic Geometry_Dr. Ngoc Cuong Nguyen

posted Nov 13, 2017, 9:36 PM by Eunyoung Choi   [ updated Nov 19, 2017, 10:50 PM ]

- Title: On the Monge-Ampère 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 Cn, i.e., it admits a negative plurisubharmonic exhaustive function. We study the properties of the "Pluricomplex Green function" of Ω, denoted by uz(ζ), which solves the Monge-Ampère equation 
 
  (ddcuz)n = 0 on Ω \ {z}, uz(ζ) ~ log|z - ζ| near z.

 

We associate to uz a measure μz supporting on ∂Ω. In general, μz 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





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GAIA Seminar on complex Analytic Geometry_Prof. Kang-Tae Kim

posted Oct 26, 2017, 9:34 PM by Eunyoung Choi   [ updated Oct 31, 2017, 11:30 PM ]

- Title: Multidimensional complex analysis---Survey lecture III

- Speaker: Prof. Kang-Tae 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





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GAIA Seminar on complex Analytic Geometry_Prof. Kang-Tae Kim

posted Oct 22, 2017, 5:25 PM by Eunyoung Choi   [ updated Oct 31, 2017, 11:30 PM ]

- Title: Multidimensional complex analysis---Survey lecture II

- Speaker: Prof. Kang-Tae 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




                         

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GAIA Seminar on complex Analytic Geometry_Prof. Kang-Tae Kim

posted Sep 25, 2017, 7:44 PM by Eunyoung Choi   [ updated Sep 25, 2017, 7:46 PM ]

- Title: Multidimensional Complex Analysis through Geometry; an Introduction

- Speaker: Prof. Kang-Tae 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

                        
 

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GAIA Seminar on complex Analytic Geometry_Dr. Ngoc Cuong Nguyen

posted Sep 18, 2017, 9:20 PM by Eunyoung Choi   [ updated Sep 20, 2017, 9:42 PM ]

- 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 quasi-plurisubharmonic solution to the Monge Ampère equation if and only if it is dominated locally by Monge-Ampere 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





 

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GAIA Seminar on complex Analytic Geometry_Dr. Seungro Joo

posted Sep 17, 2017, 9:32 PM by Eunyoung Choi   [ updated Sep 17, 2017, 9:44 PM ]

- Title: Compactness of certain families of pseudo-holomorphic mapping into Cn

 

- 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 pseudo-holomorphic mapping into Cn,
Int.J.Math. 15(1) (2004), 1-12

   

- Place: GAIA Seminar Room (#106, Math Science bldg.)

 

- Date: 8 p.m. - 10 p.m on Monday, 18 september 2017

 

 

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GAIA Seminar on complex Analytic Geometry_Prof. Kang-Tae Kim

posted Aug 30, 2017, 11:27 PM by Hyemin Shin

- Title: On the squeezing function for Pseudo-convex domain in C^n

- Speaker: Prof. Kang-Tae 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.)
 
- Date: 8 p.m. - 10 p.m on Monday, 4 September 2017


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