报告人：麻小南（巴黎西岱大学）

时间：2023年12月18日16:30-17:30

地点：二教2307

题目：Bergman kernels on punctured Riemann surfaces

摘要：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 nearthe punctures, and a holomorphic line bundle that polarizes the metric. We will explain the Bergman kernel can be localized around thesingularities 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 powersof the line bundle and of the Bergman kernel of the Poincar\'e model nearthe singularity tends to one up to arbitrary negative powers of the tensor power. 

This is a joint work with Hugues Auvray and George Marinescu.