On Extension of closed complex (basic) differential forms: Hodge numbers and (transversely) $p$-K\"ahler structures
数学专题报告
报告题目(Title)：On Extension of closed complex (basic) differential forms: Hodge numbers and (transversely) $p$-K\"ahler structures
报告人(Speaker)：饶胜教授 （武汉大学）
地点(Place)：腾讯会议：711-809-795
时间(Time)：2022年5月23日下午2:30-3:30
邀请人(Inviter)：汪志威
报告摘要
Inspired by a recent work of Dingchang Wei--Shengmao Zhu on the extension of closed complex differential forms and C. Voisin's usage of the $\partial\bar\partial$-lemma, we obtain several new theorems of deformation invariance of Hodge numbers and reprove the local stabilities of $p$-K\"ahler structures with the $\partial\bar\partial$-lemma. Our approach more concerns about the $d$-closed extension by means of the exponential operator $e^{\iota_\varphi}$. Furthermore, we prove the local stabilities of transversely $p$-K\"ahler structures with mild $\partial\bar\partial$-lemma by adapting the power series method to the foliated case, which strengthens the works of A. El Kacimi Alaoui--B. Gmira and P. Ra\'zny on the local stabilities of transversely ($1$-)K\"ahler structures. This talk is based on a joint work with Runze Zhang.
主讲人简介
饶胜，武汉大学教授，2019年国家优青，研究方向复几何。饶胜教授与刘克峰教授等合作者在复几何领域多个研究方向得到重要的原创性成果。 相关论文发表在Invent. Math, Journal of algebraic geometry, JMPA, Compositio Math等著名杂志。
