中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
非线性泛函分析研讨班
Speaker: 郭琪 副教授 (中国人民大学)
Inviter: 孙黎明
Language: Chinese
Title：Nonlinear Eigenvalue Problems: From Discrete to Continuous Models
Time&Venue：2026年3月25日（星期三）15:00-16:00 & 思源楼 S615
Abstract: This talk explores nonlinear eigenvalue problems in both continuous and discrete framworks. We first analyze nonlinear Dirac equations under normalization constraints, proving existence, nonrelativistic limits toward nonlinear Schrödinger ground states, and qualitative properties such as uniform bounds and exponential decay. Then we introduce a random graph model with improved connectivity and study the first nonzero eigenvalue of its discrete Laplacian, establishing upper and lower bounds with applications to hyperbolic geometry.
Speaker: 陈露 副教授 (北京理工大学)
Inviter: 孙黎明
Language: Chinese
Title：Reconstruction by single passive observation and Sommerfeld-Rellich Framework for Scattering on Hyperbolic Space.
Time&Venue：2026年3月25日（星期三）16:00-17:00 & 思源楼 S615
Abstract: In this talk, I will first revisit the longstanding inverse problem of simultaneously recovering both causal sources and medium parameters from a single passive boundary observation, and present our recent progress on this problem. Second, I will introduce a complete time-harmonic scattering theory we have established for hyperbolic space, formulated within the classical Sommerfeld-Rellich paradigm centered on the far-field pattern. This theory is deeply connected to the physical framework of Anti-de Sitter (AdS) theory, providing a natural language for describing how bulk wave propagation is reflected in boundary observables. Our work lays the groundwork for a far-field-based approach to scattering and inversion in hyperbolic geometry.
附件：