应用数学青年讨论班（午餐会）—— New trends for p-Laplacian eigenproblems on graphs
摘要：The spectrum of the graph p-Laplacian is closely related to many combinatorial properties of the graph itself; and its eigenpairs, reveal important information about the topology and geometry of the graph. In particular, when p is equal to 1 and infinity, the p-Laplacian eigenvalues approximate the multi-way Cheeger constants and the packing radii of the graph, respectively. However, the eigenvalue problem for graph p-Laplacians is a challenging topic both theoretically and computationally. In this talk, I will present some new ingredients for studying the graph p-Laplacian eigenproblem. These include homological eigenvalues, spectral duality, and tools from signed graphs.