報告題目：Weighted $L^2$-Theory for the Dirac Operator

　　報告人：張宇晨

　　報告時間：11月20日（星期四）13：30-14：30

　　報告地點：理學院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.

　　報告人簡介：張宇晨，中科院數學與系統科學研究院博士后。主要研究方向為Clifford分析、四元數分析。在四元數分析、離散四元數分析等方面取得一系列成果。相關成果發表在JGA等國際著名數學學術期刊上。