Lectures on Chern-Weil Theory and Complex Differential Geometry
Student No.:60
Time:Wed & Fri 13:30-15:05, Sep.26-Dec.21
Instructor:Akito Futaki  [Tsinghua University]
Place:Lecture Hall, Jin Chun Yuan West Bldg.
Starting Date:2018-9-26
Ending Date:2018-12-14

The first half of this course is about basic study on connections, curvature and characteristic classes. We start with connections for vector bundles including Levi-Civita connection for Riemannian manifolds and Chern connection for Hermitian vector bundles. Then we turn to connections for general principal bundles and the theory of characteristic classes (Chern-Weil theory). In the second half of the course some recent topics on Kähler geometry will be discussed.

Prerequisite: Basic knowledge on manifolds, Lie groups and Lie algebras.

[1] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry I, II, 1996, Wiley Classics Library.
[2] S. S. Chern, Complex manifolds without potential theory, Van Nostrand Math. Series, 1967.
[3] A. Futaki, Kähler-Einstein metrics and integral invariants. Springer Lecture Notes, vol. 1314, 1988.