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# 数学学科数学研究所学术报告（饶胜 教授 武汉大学）

 报告题目：On Extension of closed complex (basic) differential forms: Hodge numbers and (transversely) $p$-K\ahler structures报告人：饶胜 教授（武汉大学）报告时间：2022年5月10日（周二）16：00-17：00报告地点：腾讯会议ID:  979-834-366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.报告人简介：饶胜，武汉大学数学与统计学院教授、博士生导师，2019年获批国家级人才项目，研究方向为多复变与复几何。与人合作在复几何领域多个研究方向得到重要的原创性成果，相关研究成果发表在Invent. Math., JAG, Compositio Math.,  JMPA等著名杂志。  邀请人：朱盛茂