Registration Deadline: September 20, 2026

Instructor: Professor Rasul Shafikov, Western University

Course Dates: 
Mid-Semester Break: 
Lecture Time: 
Office Hours: 

Registration Fee:

• Students from our Principal Sponsoring & Affiliate Universities: Free
• Other Students: CAD$500

Capacity Limit: 

Format: 

Course Description

Complex manifolds form a rich class of manifolds that connects complex analysis, differential geometry, algebraic topology, algebraic geometry, PDEs, and other branches of mathematics together. Complex manifolds have many deep applications not only in mathematics but also in physics. It is currently one of the most actively developed areas of pure mathematics that offers many open unsolved problems.

The goal of the course is to give a gentle introduction to complex manifolds, emphasizing the underlying concepts, basic geometric constructions, and outlining a number of fundamental results. The intent is to cover both Stein and projective manifolds, including the Kodaira embedding theorem. The course evaluation will be based on homework assignments.

The required background is a course in one complex variable, linear algebra, and a basic course in geometry that covers smooth manifolds.

A tentative list of topics to be covered:

1. Holomorphic functions and maps.
2. Examples of complex manifolds: projective spaces, affine and projective manifolds, tori, complex submanifolds, Stein manifolds, and more.
3. Holomorphic vector bundles; divisors and line bundles.
4. Differential calculus and the Dolbeault complex.
5. Sheaves and sheaf cohomology.
6. Kähler manifolds.
7. Hodge theory and the Kodaira embedding theorem.

Main references:

1. John M. Lee. Introduction to complex manifolds. AMS Graduate Studies in Mathematics, Volume: 244; 2024; 361 pp (Main textbook)
2. Daniel Huybrechts. Complex geometry, an introduction. Springer-Verlag, Berlin, 2005.
3. R. O. Wells, Jr. Differential Analysis on Complex Manifolds. Springer-Verlag, GTM 65.