报告题目：Nonlinear Hodge Flows in Symplectic Geometry
报告人：何维勇 教授 (University of Oregon)
邀请人：江瑞奇
报告时间：2023-06-29（星期四）10:00-11:00 数学院425
报告内容：A folklore problem in symplectic geometry: whether two symplectic forms in a given symplectic class on a compact symplectic four manifold are isotropic to each other. This problem is completely open at the moment and it is one of the fundamental problems in symplectic geometry. Applying the Hodge theory in a nonlinear way, we introduce a family of nonlinear Hodge flow, which gives an approach to answer the question. We study a conformal Hodge flow in detail, proving a stability result and long time existence criteria.
报告人简介：何维勇教授的研究方向为微分几何，几何分析，几何偏微分方程。他在复几何（Calabi flows，Extremal Kahler metrics），Sasaki 几何， 几何偏微分方程（复蒙日-安培方程，Donaldson 方程， Gursky-Streets方程等），以及近复几何，高阶椭圆和抛物型偏微分方程等领域取得了领先的前沿结果，结果发表在Comm. Pure Appl. Math.，Amer. J. Math.，Math. Ann.，Adv. Math.，Forum Math. Sigma，Trans. Amer. Math. Soc.，J. Funct. Anal.等学术期刊上。
