"Geometry and Analysis on Groups" Research Seminar
Coarse Helly property and distance formulae.
Mark Hagen (University of Bristol)
A basic fact about Gromov-hyperbolic spaces is that, given n points,
the "quasiconvex hull" of those points is quasi-isometric to
a finite tree, with constants depending on n. A theorem of
Behrstock-Hagen-Sisto says that this generalises in a natural way: in
a "hierarchically hyperbolic space", the same holds, except one has to use CAT(0) cube complexes instead of trees. I will discuss some extra conditions under which this approximation can be made uniform, and give some group-theoretic applications, which are joint work with Harry Petyt.