学术报告报告主题: Relativistic and Discrete Eigenvalue Problems
报 告 人: 郭琪
报告时间：2025年 10月27日（星期一）下午14:00-15:00
报告地点：37号楼 3A02
邀 请 人: 陈波 副教授
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数学学院
2025年10月21日
报告摘要：
In this talk, I will present several distinct eigenvalue problems and explore their interconnections. The first problem concerns the existence of ground states for the nonlinear Dirac equation with power-type nonlinearities. I will demonstrate that, in the nonrelativistic limit, these Dirac ground states converge to the nonlinear Schrödinger ground states. The second problem involves the eigenvalue problem of the discrete Laplacian on a newly introduced random graph model, which features a higher number of connected graphs. I will examine bounds for the first eigenvalue of the discrete Laplacian and discuss an application in geometry.
报告人介绍：
郭琪，中国人民大学讲师，2021年博士毕业于中科院数学所，研究方向为临界点理论、变分法和随机图理论等，近年来主要关注Dirac方程与离散逼近等问题，主持博士后基金一项，国家自然科学基金（青年项目）一项，相关研究工作发表在JDE, SIMA, CVPDE, DCDS, JMP等杂志。