【数学与统计及交叉学科前沿论坛------高端学术讲座第148场】
报告题目：The Schwarz lemma on complex Finsler manifolds
报 告 人：邱春晖 厦门大学教授
报告时间：3月14日周五下午15：30-16：30
报告地点:阜成路校区教二楼302室
报告摘要: The classical Schwarz lemma is one of the core contents of complex analysis and one of the most beautiful results in complex analysis. It has widespread applications and profound implications. Many famous mathematicians have explored the Schwarz lemmas and their applications from the perspectives of both function theory and differential geometry. In this talk, we generalize the Schwarz lemma to complex Finsler manifolds. As an application, we give a rigidity result.
This work is joint with Jinling Li and Qixin Zhang.
报告人简介：邱春晖博士，厦门大学数学科学学院教授，博士生导师。主要研究多复变函数论和复Finsler几何，在Adv. Math.，Math. Z, J. Geom. Anal.等发表论文60多篇。主持（过）国家自然科学基金重点项目一项、面上项目七项、 数学“天元”基金项目五项。荣获2018年国家级教学成果二等奖（排名第五），2017年福建省第八届高等教育教学成果特等奖（排名第五）。曾担任厦门市数学学会会长。培养了30多位博士和硕士。多次组织多复变与复几何、Finsler几何学术会议和研究生暑期学校, 多次在国际会议和全国性学术会议上做邀请报告。
报告题目：On the generalized $L^p$ Bergman theory
报 告 人：张利友 首都师范大学教授
报告时间：3月14日周五下午16：30-17：30
报告地点:阜成路校区教二楼302室
报告人简介：张利友，2007年于首都师范大学获得博士学位，2007-2009年进入中科院数学所博士后流动站，2009年出站后到首都师范大学工作至今。现为首都师范大学数学科学学院教授，博士生导师，研究方向为多复变与复几何。
报告摘要: In this talk, we will present recent developments in the $L^p$ Bergman theory, highlighting its differences from the classical $L^2$ case. A central focus will be on the regularity of the $L^p$ Bergman kernel. We will demonstrate that, in contrast to the $L^2$ Bergman kernel, the $L^p$ Bergman kernel is generally not real-analytic on certain bounded domains in $\mathbb{C}^n$. This reveals the fundamental distinction between the $L^p$ and $L^2$ kernels.
We will also explore the geometric aspects of the $L^p$ Bergman theory. In particular, we will show that as $p$ approaches to infinity, the $L^p$ Bergman metric converges to the Caratheodory metric. Additionally, we will examine the Levi form of the $L^p$ Bergman kernel, in the sense of current, and prove that it is bounded below by the Bergman metric for $p>2$ and by the Caratheodory metric for $p<2$.
If time permits, we will also discuss stability results for weighted $L^p$ Bergman kernels, and their connections to the (strong) openness conjecture.
