Coboundary Expansion Inside Chevalley High-Dimensional Expanders

Explore a computer science and discrete mathematics seminar focusing on coboundary expansion in Chevalley high-dimensional expanders. Ryan O'Donnell from Carnegie Mellon University examines the topological properties of coset complex high-dimensional expanders (HDXs) over Chevalley groups, extending beyond the commonly studied A_d-type constructions. Learn how O'Donnell and collaborator Noah G. Singer obtained the "B-type" generalization of Kaufman-Oppenheim's result on A_3-type coset complex HDXs, demonstrating good 1-coboundary expansion in their links to yield 2-dimensional topological expanders. Discover the intersection of topological considerations with group theory, including how they overcame challenges through computer-assisted rank computations and group-theoretic calculations that have been Lean-verified. Understand the growing importance of sparse high-dimensional expanders in theoretical computer science, particularly their applications in property testing and probabilistically checkable proofs.