### High dimensional expanders

Combinatorics Seminar

2nd February 2021, 3:00 pm – 4:00 pm

Virtual (online) Zoom seminar; a link will be sent to the Bristol Combinatorics Seminar mailing list and the Bristol Analysis & Geometry mailing list, the week before the seminar.

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 results in a positive answer to this question (according to Gromov's 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. If time permits, I will mention recent application of this theory to problems in the theory of quantum error correcting codes. This talk is based on a joint work with Tali Kaufman.

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