讲座题目：The regularity of weakly Dirac-harmonic maps into pseudo-Riemannian manifolds

主办单位：三峡数学研究中心/理学院

报告专家：艾万君博士（西南大学）

报告时间：202X年4月22日（周五） 下午（14:30—17:30）

报告地点：腾讯会议（ID： 176 358 895）

专家简介：艾万君，2017年毕业于中国科学技术大学。随后，在上海交通大学从事博士后研究工作。现任职于西南大学数学与统计学院。 承担重庆市面上项目、中央高校基本科研业务费项目各一项。参与国家自然科学基金面上项目两项、国家自然科学基金数学天元基金项目一项。主要研究领域为调和映射及其相关领域。相关研究结果发表在J. Func. Anal.、Calc. Var. PDE.、Sci. China Math.、Ann. Global Anal. Geom. 等杂志上。

报告摘要：Dirac-harmonic maps are motivated by the supersymmetric nonlinear sigma modelin quantum field theory, which generalize the classical harmonic maps and harmonic spinors. In recent decades, the existence, regularity, and blow-up analysis of Dirac-harmonic maps from a Riemann surface to another compact Riemannian manifold have been extensively studied. In this presentation, we will start from classical regularity results of spherical harmonic maps and Lorentz spherical harmonic maps, and then show some generalizations of these results for general target manifolds, both in Riemannian and Lorentzian cases. Finally, we present a new result about the regularity of Dirac-harmonic maps from Riemann surfaces into stationary Lorentzian manifolds. It turns out the regularity of weakly Dirac-harmonic maps depends on a general regularity theorem of critical elliptic systems without an L2-antisymmetric structure. Our results generalizethe corresponding regularity results of Hélein, Rivière and Rivière-Struwe for harmonic maps. This is joint work with Zhu, Miaomiao.