445-2 - Differential Geometry

Tuesday 3:00pm - 3:50pm, Lunt 103
Thursday 1:00pm - 2:40pm, Lunt 103
Course website: www.math.northwestern.edu/~tosatti/cy.html

Instructor:

Valentino Tosatti
Email: tosatti@math.northwestern.edu
Office: Lunt 225

Office hours:

Monday 3:00pm-4:00pm

Course Contents:

This course is an introduction to Calabi-Yau manifolds. Topics that will likely be covered include:

Prerequisites:

Familiarity with basic differential and Riemannian geometry and complex analysis. We will use some results about PDE from the course 420-1.

Textbook:

We will not follow any textbook directly, but the following references might be useful when studying: The following are some other textbooks that contain basic material on complex and Kähler manifolds, but which have a possibly different focus:

Grading:

There will be regular homework.

Daily Schedule:

This is a tentative syllabus and it is likely to change as the course progresses.

Date Topics Covered Remarks
Jan. 8, 10 Complex Manifolds
Jan. 15, 17 Hermitian metrics Homework 1
Due January 22 in class
Solution
Jan. 22, 24 Kähler metrics Homework 2
Due January 29 in class
Solution
Jan. 29, 31 Ricci curvature Homework 3
Due February 5 in class
Solution
Feb. 5, 7 Proof of the Calabi Conjecture Homework 4
Due February 12 in class
Solution
Feb. 12, 14 Proof of the Calabi Conjecture Homework 5
Due February 19 in class
Solution
Feb. 19, 21 Proof of the Calabi Conjecture Homework 6
Due February 28 in class
Solution
Feb. 26, 28 Chern number inequalities, uniqueness of CP2 Homework 7
Due March 5 in class
Solution
Mar. 5, 7 Albanese map for compact Kähler manifolds Homework 8
Due March 12 in class
Solution
Mar. 12, 14 Structure theorem for Ricci-flat Kähler manifolds