MAGIC044: Complex Differential Geometry

Course details

A specialist MAGIC course

Semester

Spring 2009
Monday, January 19th to Friday, March 27th; Monday, April 27th to Monday, April 27th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Tuesdays
13:05 - 13:55
Thursdays
13:05 - 13:55

Announcements

October 14th: I added the first set of exercises.
November 27th: the lecture is cancelled, due to ilness
December 9th:: I have now covered all the material and so the course is finished.

Description

Complex manifolds are central objects in many areas of mathematics: differential geometry, algebraic geometry, several complex variables, mathematical physics, topology, global analysis etc. Their geometry is much richer than that of real manifolds which leads to fascinating phenomena and the need for new techniques.
The present course will give a brief introduction to basic notions and methods in complex differential geometry and complex algebraic geometry. The aim is to present beautiful and powerful classical results, such as the Hodge theorem, as well as to develop enough language and techniques to make the material of current interest accessible.

Prerequisites

Familiarity with basic notions of topological and differentiable manifolds, especially tensors and differential forms.
Knowledge of such Riemannian concepts as the Levi-Civita connection and curvature will be helpful, but not essential.

Syllabus

1. Complex and almost complex manifolds
2. Holomorphic forms and vector fields
3. Complex and holomorphic vector bundles
4. Hermitian bundles, metric connections, curvature
5. Chern classes
6. Hermitian and Kähler metrics
7. Dolbeaut theory and the Hodge theorem
8. Curvature of Kähler manifolds; holomorphic sectional and Ricci curvature

Lecturer

  • RB

    Professor Roger Bielawski

    University
    University of Leeds

Bibliography

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Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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