The convexity of Bergman kernels

讲座题目：The convexity of Bergman kernels
讲座时间 Datetime:2024年10月21日 15：00—16：30；10月23日 10：00—11：30；10月24日 19：30—21：00
地点 Venue: 中大珠海校区海琴二号A412-2
报告人Speaker:熊渊朴 博士后
单位 Affiliation: 复旦大学数学科学学院
主持人 Host：徐行
报告摘要 Abstract:
If \Omega is a convex domain in \mathbb{C}, a result going back to Caffarelli-Friedman and Minda shows that \log \lambda_{\Omega}(z) is also convex, where \lambda_{\Omega}(z) is the density of hyperbolic metric. This result can be generalized to the high dimensional case via Bergman kernels. More precisely, if \Omega is a convex domain in \mathbb{C}^n and \varphi is a convex function on \Omega, then \log K_{\Omega, \varphi}(z) is convex. The proof makes use of Oka's trick and Berndtsson's subharmonicity theorem.
We will discuss the topic in full details in three talks. In the first talk, I will introduce some background and the idea of the proof. In the second talk, I will present Berndtsson's proof of his subharmonicity theorem. The proof of the main result will be given in the last talk.                     

报告人简介：
熊渊朴，复旦大学博士后。2023年博士毕业于复旦大学。主要研究方向为多复变函数论。在CVPDE, Proc. AMS等著名期刊发表多篇学术论文。