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Thursday, August 3, 2017

Geometry, Groups, and Dynamics/GEAR
12:00 pm   in 241 Altgeld Hall,  Thursday, August 3, 2017
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Submitted by clein.
 Alessandro Sisto (ETH Math)Quasiflats in hierarchically hyperbolic spacesAbstract: The notion of hierarchically hyperbolic space provides a common framework to study mapping class groups, Teichmueller spaces with either the Teichmueller or the Weil-Petersson metric, CAT(0) cube complexes admitting a proper cocompact action, fundamental groups of non- geometric 3-manifolds, and other examples. I will discuss the result that any top-dimensional quasi-flat in a hierarchically hyperbolic space lies within finite Hausdorff distance from a finite union of ”standard orthants”, a result new for both mapping class groups and cube complexes. Also, I will discuss how this can be used to reduce proving quasi-isometric rigidity results to much more manageable, (mostly) combinatorial problems that require no knowledge about the geometry of HHSs. Joint work with Jason Behrstock and Mark Hagen.