In the recent theory of high dimensional expanders, the following open problem was raised by Gromov: Are there bounded degree high dimensional expanders?

For the definition of high dimensional expanders, we shall follow the pioneers of this field, and consider the notions of coboundary expanders (Linial-Meshulam) and topological expanders (Gromov).

In a recent work, building on an earlier work of Kaufman-Kazhdan-Lubotzky in dimension 2, we were able to prove the existence of bounded degree expanders according to Gromov, in every dimension.

In this talk I will present an outline of the proof of this result, focusing on a new local-to-global criterion of high-dimensional expansion.

This is a joint work with Tali Kaufman

## Date:

Mon, 25/12/2017 - 14:00 to 16:00