High-Dimensional Expanders - How I Learned to Stop Worrying and Love Group-Theoretic Constructions

Explore high-dimensional expanders and group-theoretic constructions in this 47-minute talk. Delve into the intricacies of 2-dimensional expanders, graphs of constant link, and the challenges in finding them. Discover the motivations behind using group theory to construct high-dimensional expanders (HDXes). Gain insights into the Classification of Finite Simple Groups and its relevance to the topic. Learn about expander graphs, the concept of link in a vertex, and the work of Cristina Ballantine. Examine new research conducted with Kevin Pratt and understand why Abelian groups fail to create 2-dimensional expanders. This presentation, based on joint work with Kevin Pratt, offers a comprehensive look at the intersection of group theory and high-dimensional expanders.

Intro
Expander Graphs in One Slide
the Link of a vertex
High-Dimensional Expanders
2-Dimensional Expanders
Graphs of constant link L
Hero #1 Cristina Ballantine
New work with Kevin Pratt
Classification of Finite Simple Groups
Abelian groups failing to create 2-dim. expanders