走向现代数学学术报告 - 李小山副教授（No. 694）

题目：Semi-classical asymptotics of partial Bergman kernels on R-symmetric complex manifolds with boundary

报告人: 李小山 副教授（武汉大学）

时间：2024年4月24日 9:40

腾讯会议ID：761-599-631

摘要：Let M be a relatively compact connected open subset with smooth connected boundary of a complex manifold M'. Let (L, h^L) be a positive line bundle over M'. Suppose that M' admits a holomorphic R-action which preserves the boundary of M and lifts to L. In this talk, we will show an asymptotic expansion of a partial Bergman kernel associated to a package of Fourier modes of high frequency with respect to the R-action in the high powers of L. As an application, we establish an R-equivariant analogue of Fefferman's and Bell-Ligocka's result about smooth extension up to the boundary of biholomorphic maps between weakly pseudoconvex domains in C^n. Another application concerns the embedding of pseudoconcave manifolds. This talk is based on a joint work with Chin-Yu Hsiao and George Marinescu.

报告人简介：李小山副教授2013年博士毕业于武汉大学，之后在台湾中研院数学所做博士后研究，2014年至今任教于武汉大学。李小山副教授主持国家自然科学基金面上项目两项、国际（地区）合作与交流项目一项，论文发表在TAMS, Math. Z., IMRN, MRL, Math. Ann., JFA等众多国际数学著名期刊。