Math 230A: Differential Geometry (Fall 2019)

Class Time: Tuesdays and Thursdays 9-10:15am, Science Center 310

Instructor: Sébastien Picard
Email: spicard@math
Office: Science Center 235
Office hours: Wednesday 2-3pm and Thursday 12-1pm, or by appointment

Course Assistant: Or Eisenberg
Email: oreisenberg@college
Office Hours: Thursdays 6pm in Eliot Dining Hall

Syllabus: Can be found here.

Course Description: Introduction to bundles, connections, metrics, and curvature.

Textbook: Clifford Henry Taubes, Differential Geometry

Problem Sets: Weekly homework problem sets will be posted below. Homework is due on Thursdays, submitted on Canvas.

Homework 1 - Due September 12
Homework 2 - Due September 19
Homework 3 - Due September 26
Homework 4 - Due October 3
Homework 5 - Due October 10
Homework 6 - Due October 17
Homework 7 - Due October 24
Homework 8 - Due October 31
Homework 9 - Due November 7
Homework 10 - Due November 14
Homework 11 - Due November 21

Final Exam: There will be a take-home final exam.

Grading Scheme:
60% Homework
40% Final

Schedule:
Sept 3, 5: Review of Manifolds [Taubes, Chapter 1]
Sept 10, 12: Lie groups [Taubes, Chapter 2]
Sept 17, 19: Vector bundles [Taubes, Chapter 3-4]
Sept 24, 26: Maps and vector bundles [Taubes, Chapter 5]
Oct 1, 3: Complex vector bundles and metrics [Taubes, Chapter 6-7]
Oct 8, 10: Geodesics [Taubes, Chapter 8]
Oct 15, 17: More geodesics [Taubes, Chapter 9]
Oct 22, 24: Levi-Civita connection [Taubes, Chapter 15]
Oct 29, 31: Riemann curvature tensor [Taubes, Chapter 16]
Nov 5, 7: Principal bundles [Taubes, Chapter 10]
Nov 12, 14: Connections on principal bundles [Taubes, Chapter 11-12]
Nov 19, 21: Characteristic classes [Taubes, Chapter 14]
Nov 26, Dec 3: Yang-Mills functional