Simple High Dimensional Expanders from Cayley Graphs

Join a computer science and discrete mathematics seminar featuring Yotam Dikstein from the Institute for Advanced Study as he explores the construction of High Dimensional Expanders (HDXs) from Cayley graphs. Dive into the world of expander graphs, understanding their role as sparse yet well-connected structures fundamental to theoretical computer science and combinatorics. Learn how HDXs serve as hypergraph analogues with applications in coding theory, PCPs, Boolean function analysis, and extremal combinatorics. Discover new constructions of HDXs derived from Cayley graphs over Fn2, building upon Louis Golowich's work and exploring connections to the Grassmannian. Gain insights into expanding sparsifications of the Grassmannian through elementary arguments about Johnson graphs and subspaces of Fn2. Begin with a comprehensive introduction to HDXs, covering definitions, constructions, and applications, making the content accessible to those without prior HDX knowledge.