Solving equations with Hodge theory
Student No.:100
Time:Fri 16:30-17:30, 2017.9.22
Instructor:Liu Kefeng (Presented by Yang Xiaokui)  
Place:Lecture hall, 3rd floor of Jinchun Yuan West Building
Starting Date:2017-9-22
Ending Date:2017-9-23

Abstract: We will discuss several new applications of Hodge decomposition.
First by using operators from $L^2$-Hodge theory we present a simple method to solve the Beltrami equations for quasi-conformal maps, and give a simple proof of the Newlander-Nirenberg theorem for the existence of complex analytic coordinates for integrable almost complex structures.Then we use operators from Hodge theory to give a closed formula for certain canonical sections of Hodge bundles on marked and polarized moduli spaces of projective manifolds.