Higher-Dimensional Expansion of Random Geometric Complexes
Explore the concept of higher-dimensional expansion in random geometric complexes through this lecture by Tselil Schramm from Stanford University. Delve into the generalization of graph expansion to hypergraphs and simplicial complexes, focusing on 2-dimensional spectral expansion. Examine how local expansion of vertex links and neighborhoods can indicate global expansion. Investigate the open question of whether sparse 2-dimensional expanders are abundant or rare in nature. Learn about new evidence supporting their abundance, including findings on triangles in random geometric graphs on high-dimensional spheres forming expanding simplicial complexes. Gain insights into this collaborative research with Siqi Liu, Sidhanth Mohanty, and Elizabeth Yang, which contributes to the field of structural results in geometric complexes.