Curvature, Swan's Theorem and Similarity Classification of Holomorphic Bundles

Chunlan Jiang  (Hebei Normal University)

10:00 am to 11:00 am, Apr 11th, 2014   Science Building A1510




Abstract:

In 1978, M. I .Cowen and R. G. Douglas gave a successful unitarily classification for Hermitian holomorphic vector bundle by using the curvature function. In the same paper, they also raised the similarity classification problem. Specially, in 2009,R. G. Douglas asked the following question: Can one give conditions involving the curvatures which imply that two quasi-free Hilbert modules of multiplicity one are similar?

In this paper, we introduce a class of Hermitian holomorphic vector bundle called as quasi-homogeneous bundle which contains all of the homogeneous bundles and some weak homogenous bundles and give the completely similarity classification theorem of quasi-homogeneous bundles by using curvature functions and the second fundamental forms.

About the speaker:

蒋春澜现任河北师范大学校长。教授,博士生导师。九三学社第十三届中央委员会委员,河北省第七届委员会副主委。河北省第十一届政协常委。

蒋春澜教授主要从事算子代数可约与强不可约性研究。1998年英国皇家科学院会员S.Power向世界著名的英国朗文出版公司推荐出版了红皮书研究专著《Strongly irreducible operators on Hilbert space》。美国著名算子理论家D.A.Herrero在专著《Approximation of Hilbert Space Operators》将蒋的结果作为一节列出,该书是美国算子理论界研究生的通用教材。作者在书中评论蒋的结果是80年代算子理论的十大重要结果之一。蒋春澜教授现承担《国家重点基础研究发展规划》(973计划)项目的研究,国家基金委重点基金项目,国家教育部《高等学校数学研究与高等人才培养中心》研究项目。蒋春澜教授应邀多次到国内外讲学并在国际学术会议上作报告。

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