Explore algorithms and hardness results for linear algebra on geometric graphs in this theory seminar. Delve into efficient spectral graph theory for k-graphs, examining problems like matrix-vector multiplication, spectral sparsification, and Laplacian system solving. Investigate the relationship between function parameters and algorithmic efficiency, considering SETH-based hardness results. Learn about the limitations of the fast multipole method and its dimensional dependence. Gain insights into well-separated pairs decomposition, approximate nearest neighbors, and open problems in the field of geometric graph algorithms.