讲座题目：Donaldson Question: “Tamed to Compatible”

主办单位：三峡数学研究中心/理学院

报告专家：王宏玉 教授

报告时间：2024年4月11日（星期四）16：30

报告地点：三峡数学研究中心L1218

专家简介：王宏玉，扬州大学数学科学学院教授，主要研究方向为微分几何、偏微分方程及低维拓扑。近年来，主要从事度量几何、辛几何和非线性发展方程的研究。

报告摘要：In this talk, we show that on any tamed closed almost complex fourmanifold (M, J) whose dimension of J-anti-invariant cohomology is equal to self-dual second Betti number minus one, there exists a new symplectic form compatible with the given almost complex structure J. In particular, if the self-dual second Betti number is one, we give an affirmative answer to Donaldson question for tamed closed almost complex four-manifolds. Our approach is along the lines used by Buchdahl to give a unified proof of the Kodaira conjecture. Thus, our main result gives an affirmative answer to the Kodaira conjecture in symplectic version.