数学学科2025系列学术报告之二十六

　　报告题目：Weighted $L^2$-Theory for the Dirac Operator

　　报告人：张宇晨

　　报告时间：11月20日（星期四）13：30-14：30

　　报告地点：理学院1-301

　　英文摘要：In this talk, we revisit the weighted $L^2$-theory for the Dirac operator established by professor Ji Qingchun and Zhu Ke. We then demonstrate that the classical $L^2$-existence theorem—valid for domains in $\mathbb{R}^2$ under a subharmonic weight condition—fails in higher dimensions. Finally, we present an improvement upon the results of Ji and Zhu by deriving a refined a priori estimate, thereby overcoming the restrictive structural conditions previously imposed on the weight function.

　　报告人简介：张宇晨，中科院数学与系统科学研究院博士后。主要研究方向为Clifford分析、四元数分析。在四元数分析、离散四元数分析等方面取得一系列成果。相关成果发表在JGA等国际著名数学学术期刊上。