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GAIA Seminar on Complex Analytic Geometry - Seungjae Lee

posted Nov 19, 2015, 4:27 PM by Hyemin Shin   [ updated Nov 19, 2015, 4:55 PM ]

- Title: Rigidity of Bergman kernel under holomorphic immersion map

- Speaker: Seungjae Lee (POSTECH)

- Abstract: It is well known that Bergman kernel is invariant under biholomorphic maps between two bounded complex domains, but it is not invariant under non one-to-one holomorphic immersion. Since Bergman kernel is depend on L2 holomorphic spaces of these domains, in this case, the proof of this phenomena is not so hard.    

But it seems to be that theorems related to this phenomena is not yet established in non-compact complex manifold case. The main reason of this absence is, in general, to compare between the space of pullbacked L2 holomorphic forms and the space of original L2 holomorphic forms is not so easy rather than domain cases. 

In this talk, I want to show that this phenomena is true between two some open Riemann surface cases by overcoming this difficulties.

Also if time is permitted I will explain that R.C. Gunning and R. Narasimhan’s theorem: “Any connected open Riemann surface has a holomorphic immersion into some complex plane.” 

- Place: GAIA Seminar Room (#106, Math Science bldg.)
- Date: 8 p.m. - 10 p.m on Monday, 23 November 2015

Poster <---- click