Dan Berlyne (*extra, special second talk!*)

Graph products as hierarchically hyperbolic groups

Direct products and free products are two of the simplest ways
of combining groups, yet they give rise to interesting geometry. Direct
products of the integers are commonly realised as lattice points in
Euclidean space, while free products of the integers exhibit hyperbolic
geometry. What happens when we mix free products with direct products?
This forms what is known as a graph product, which has geometry
somewhere in between Euclidean and hyperbolic; it is hierarchically
hyperbolic. We construct this geometry explicitly, answering two
questions of Behrstock, Hagen and Sisto. This is joint work with Jacob
Russell.