Program
Topics in geometric analysis
Student No.:50
Time:【Updated】Thu 15:10-17:00, 17:10-19:00, 2017-03-07~ 2017-06-01 (No classes on public holidays)
Instructor:Yuguang Zhang  [Tsinghua University]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-3-7
Ending Date:2017-6-1

 

 

Description:

 

 

I will give an introduction to some topics in geometric analysis. I’m planning to talk about the Calabi-Yau theorem for the existence of Kahler-Einstein metrics, K-stabilities, Bergman kernels, special lagrangian submanifolds, and the semi-flat mirror construction etc. The goal of this lecture is to introduce the basic knowledge for understanding the statements of some central conjectures in the field, for example the Yau-Tian-Donaldson conjecture and the differential geometric aspect of the Strominger-Yau-Zaslow conjecture.

 

 

 

Prerequisite:

 

 

Riemannian geometry, elliptic partial differential equation, and some basic algebraic geometry.

 

 

 

Reference:

 

 

G. Szekelyhidi, An introduction to extremal Kahler metrics, AMS.

 

 

D. Joyce,  Riemannian holonomy groups and calibrated geometry, Oxford.

 

 

M. Gross, D. Huybrechts,  D.Joyce,  Calabi-Yau manifolds and related geometries, Springer.