中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

综合报告会

（Colloquium）

报告人：  刘克峰 教授（UCLA）

题  目：Solving equations with Hodge theory

时  间：2017.09.18（星期一），16:00-17:00

地  点：数学院南楼N913室

摘要：

We will discuss several new applications of Hodge decomposition. First by using operators from L²-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.