报告题目：Solving equations with Hodge theory

报告摘要：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.