讲座主题：Constructing stable Hilbert bundles with irrational slopes

专家姓名：马飙

工作单位：北京大学北京国际数学研究中心

讲座时间：2025年06月30日 15:00-16:00

讲座地点：数学院大会议室341

主办单位：烟台大学数学与信息科学学院

内容摘要：

On any complex smooth projective curve with positive genus, we construct Hilbert bundles that admit Hermitian-Einstein metrics with irrational slopes. A main constructive step is by investigating the arithmetic property of the upper half plane in Bridgeland's definition of stability conditions. The main analytic ingredient in our proof is a notion called a well-approximation stable bundle. This notion helps us to apply the Diophantine approximation to Donaldson's functional and bound the L∞ norm of Hermitian-Einstein metrics. We further study smooth and holomorphic structures on such Hilbert bundles, and their connections to noncommutative geometry. This talk is based on a work joint with Yucheng Liu.

主讲人介绍：

马飙，现为北京国际数学研究中心博士后。研究方向为几何分析。