Mathematics G4403. Modern Geometry II, Spring 2012

Instructor: Chiu-Chu Melissa Liu
E-mail: ccliu@math.columbia.edu, ccl2121@columbia.edu
Office: 623 Mathematics Building
Phone: (212) 854-2499
Office Hours: Monday 4-6pm, Wednesday 4-5pm, or by appointments.

Lectures: Monday & Wednesday, 2:40-3:55pm, 307 Mathematics Building

Teaching Assistant: Tristan Clifford Collins
E-mail: tcollins@math.columbia.edu, tcc2119@columbia.edu
Office: 408 Mathematics Building
Phone: (212) 854-5881

Roundtable Friday 5-6pm, Mathematics 507

Textbook: [dC] Manfredo Perdigao do Carmo, Riemannian Geometry

References:

• [GHL] Sylvestre Gallot, Dominique Hulin, Jacques Lafontaine, Riemannian Geometry, third edition
• [CE] Jeff Cheeger and David G. Ebin, Comparison Theorems in Riemannian Geometry
• [KN] Shoshichi Kobayashi and Katsumi Nomizu, Foundations of Differential Geometry I & II
• [M] Shigeyuki Morita, The Geometry of Differential Forms
• [PT] Thomas Parker, Clifford Taubes, "On Witten's Proof of the Positive Energy Theorem," Comm. Math. Phys. 84 (1982), no.2, 223-238.
• [W] Edward Witten, "A New Proof of the Positive Energy Theorem," Comm. Math. Phys. 80 (1981), no.3, 381-402.

Syllabus: Tentative Syllabus

Grading: Homework 40%, Midterm 20%, Take Home Final 40%

• Homework: There will be weekly assignments, due in class on Mondays.
  The total score of each assignment is 50; late penalty is -4 points per day.
  The lowest homework score will be dropped.
  Assignment 12 (due 1/30), Assignment 13 (due 2/6), Assignment 14 (due 2/13), Assignment 15 (due 2/20),
  Assignment 16 (due 2/27), Assignment 17 (due 3/5), Assignment 18 (due 3/26), Assignment 19 (due 4/2),
  Assignment 20 (due 4/9), Assignment 21 (due 4/16), Assignment 22 (due 4/23)
• Midterm: Wednesday, March 7, 2012, in class.