Course Information

• Class Number 35240
• Catalog 2801
• Assoc 1020
• Short Title: Differential Geometry 2
• Room: Bendm 522
• Days: MWF
• Time: 11:00-11:50
• Instructor: Hales
• coursepage: http://code.google.com/p/mathcourse/
• lecture schedule

Differential Geometry

Text: Riemannian Geometry and Geometric Analysis, Jost, Fifth Edition, 2008.

Course Description

This is a course on the differential geometry of Riemannian manifolds. The course will start with the fundamental structures of Riemannian geometry, such as Riemannian metrics, geodesics, connections, curvature, and Jacobi fields. Other topics will include de Rham cohomology and harmonic forms, symmetric spaces, Kaehler manifolds, symplectic manifolds, flows, an introduction to Morse theory and Seiberg-Witten invariants.

Evaluation

Students may choose among various options for evaluation. * Paper option: two essays on topics of the student's choice, each about 15 pages in length * Oral exam option: two oral examinations on the background reading for lectures * Homework project option: three major homework projects.