### Graph products as hierarchically hyperbolic groups

Algebra and Geometry Seminar

9th October 2019, 4:00 pm – 5:00 pm

Fry Building, G.13 (note the unusual room)

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.

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