|The Calabi-Yau Theorem and some generalizations|
|Time：||Mon/Wed 15:10-17:00, 2014-08-06 ~ 2014-09-01|
|Instructor：||Valentino Tosatti [Northwestern University]|
|Place：||Conference Room 1, Floor 1, jin Chun Yuan West Building|
Sixty years ago Eugenio Calabi formulated his famous conjecture about prescribing the Ricci curvature of a Kähler metric on a compact Kähler manifold, and this was finally confirmed to be true by Shing-Tung Yau in a landmark tour de force work in 1976. In this course I will give a proof of the Calabi-Yau Theorem and derive some of its striking corollaries. Then, I will discuss some very recent generalizations of this theorem to non-Kähler Hermitian manifolds, due to Ben Weinkove and myself, including the solution of the complex Monge-Ampère equation on all compact complex manifolds.
A basic knowledge of differential geometry and complex analysis.
For the basic theory of complex and Kähler manifolds, the book "Complex Geometry: an Introduction" by D. Huybrechts is a good reference. For the proof of the Calabi-Yau Theorem and its generalizations, we will follow the original papers by Yau, Tosatti-Weinkove.