High dimensional expanders
Expander graphs are graphs which simultaneously are both sparse and highly connected. The theory of expander graphs received a lot of attention in the past half a century, from both computer science and mathematics. In recent years, a new theory of high dimensional expanders have emerged. In his seminal work, Gromov raised the following main question: Do (bounded degree) high dimensional expanders exist? A culmination of several works by experts in the field resulted in a positive answer to Gromov's question (according to his definition).
In this talk, I will give a quick introduction to the theory of high dimensional expanders, describe the challenges this theory offers, and explain the known techniques to construct such (bounded degree) high dimensional expanders.
This talk is based on a joint work with Tali Kaufman.