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SUMMARY:Real cubings and asymptotic cones - Mark Hagen (University of Bris
 tol)
DTSTART:20250708T104500Z
DTEND:20250708T114500Z
UID:TALK232822@talks.cam.ac.uk
DESCRIPTION:Median metric spaces are a common generalisation of real trees
  and CAT(0) cube complexes. &nbsp\;A real cubing is a median space arising
  as a subalgerba of a (generally infinite) product of real trees determine
 d by a (generally infinite) system of consistency conditions on pairs of c
 oordinates. &nbsp\;When the real trees are unit intervals\, one recovers C
 AT(0) cube complexes as examples of real cubings. &nbsp\;The definition ca
 n also be seen as a fine-geometric analogue of the notion of a hierarchica
 lly hyperbolic space\, with the real trees playing the role of "curve grap
 hs" and the consistency conditions playing the analogous role to the Behrs
 tock inequality. &nbsp\;\nOur first result says that any asymptotic cone o
 f a hierarchically hyperbolic space is bilipschitz equivalent to a real cu
 bing\; this generalises/strengthens a result of Behrstock-Drutu-Sapir on m
 apping class groups. &nbsp\;I will discuss the idea of this result\, which
  relies on the theory of measured wallspaces. &nbsp\;I will then discuss o
 ur main application\, to uniqueness (up to bilipschitz equivalence) of asy
 mptotic cones of various hierarchically hyperbolic groups\, like mapping c
 lass groups and RAAGs. &nbsp\;\nThis talk is on joint work in progress wit
 h Montserrat Casals-Ruiz and Ilya Kazachkov (working draft: https://www.we
 scac.net/cones.html).
LOCATION:Seminar Room 1\, Newton Institute
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