Topic: expansion properties

Ryan O’Donnell presents simple explicit families of expander graphs whose analysis needs only a small amount of group theory. The lecture explains their expansion properties and shows how these constructions can lead to stronger objects, including super-expanders and non-sofic groups with property (T).

Expansion properties of low-dimensional links can propagate through a simplicial complex. This talk presents recent results for partite high-dimensional expanders and their consequences for approximate sampling. It explains how Lorentzian and log-concave polynomials provide the mathematical basis for these local-to-global arguments.