报告题目：Bergman kernels on punctured Riemann surfaces

报告时间：2023-12-19   11:15-12:15

报 告 人 ：麻小南  教授  巴黎西岱大学

报告地点：理学院东北楼四楼报告厅（404）

Abstract：We will review our recent works on Bergman kernel on punctured Riemann surfaces. We consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincar\'e metric near the punctures, and a holomorphic line bundle that polarizes the metric. We will explain that the Bergman kernel can be localized around the singularities and its local model is the Bergman kernel of the punctured unit disc endowed with the standard Poincar\'e metric. We will explain that the quotient of the Bergman kernel of high tensor powers of the line bundle and of the Bergman kernel of the Poincar\'e model near the singularity tends to one up to arbitrary negative powers of the tensor power. This is a joint work with Hugues Auvrayand George Marinescu.