williamhill官网学术报告

Relativistic and Discrete Eigenvalue Problems

郭琪

（中国人民大学）

时间：2025-11-04    15:00—16:00（周二下午）

地点：沙河主楼E402

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.

报告人简介：Guo Qi is a lecturer at Renmin University of China. He received his Ph.D. from the AMSS, Chinese Academy of Sciences in 2021. His research interests include critical point theory, variational methods, and random graph theory. In recent years, he has focused primarily on Dirac equations and discrete approximation problems. His related research has been published in journals such as JDE, SIMA, CVPDE, DCDS, and JMP.

邀请人：张旭成

欢迎大家参加！