ncku-talk2014-12-11

NCTS(South)/ NCKU Math Colloquium

DATE 2014-12-11　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER 中央研究院數學研究所（蕭欽玉教授）

TITLE Semi-Classical Analysis in Complex Geometry: Bergman Kernel Asymptotics for Lower Energy Forms

ABSTRACT In my work with Marinescu at 2012, we give a semi-classical study of the complex Witten Laplacian. As an application, we obtain a full asymptotic expansion of the spectral function corresponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. From this result, we could deduce many classical results in complex geometry (eg Kodaira embedding and vanishing Theorems, Demailly's Morse inequalities, Bergman kernel asymptotics for ample line bundles). In this talk, I will first review these classical results in and show how to obtain these results from our main result.

NCTS(South)/ NCKU Math Colloquium

DATE	2014-12-11　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	中央研究院數學研究所（蕭欽玉教授）

TITLE	Semi-Classical Analysis in Complex Geometry: Bergman Kernel Asymptotics for Lower Energy Forms

ABSTRACT	In my work with Marinescu at 2012, we give a semi-classical study of the complex Witten Laplacian. As an application, we obtain a full asymptotic expansion of the spectral function corresponding to the lower part of the spectrum of the Kodaira Laplacian on high tensor powers of a holomorphic line bundle. From this result, we could deduce many classical results in complex geometry (eg Kodaira embedding and vanishing Theorems, Demailly's Morse inequalities, Bergman kernel asymptotics for ample line bundles). In this talk, I will first review these classical results in and show how to obtain these results from our main result.