[Binghamton Geometry Topology Seminar] Seminar Lunch

[Matthew R Haulmark]

Hi everyone,

Matt Durham from UC Riverside will be visiting us. If anyone is interested
in joining, we will meet around noon to go to lunch. Title and abstract
below.

Best,

Matt

*Title: Local quasicubicality and sublinear Morse geodesics in mapping
class groups and Teichmuller space*





*Abstract: Random walks on spaces with hyperbolic properties tend to
sublinearly track geodesic rays which point in certain hyperbolic-like
directions. Qing-Rafi-Tiozzo recently introduced the sublinear-Morse
boundary to more broadly capture these generic directions.In joint work
with Abdul Zalloum, we develop the geometric foundations of
sublinear-Morseness in the mapping class group and Teichmuller space. We
prove that their sublinearly-Morse boundaries are visibility spaces and
admit continuous equivariant injections into the boundary of the curve
graph. Moreover, we completely characterize sublinear-Morseness in terms of
the hierarchical structure on these spaces.Our techniques include
developing tools for modeling sublinearly-Morse rays via CAT(0) cube
complexes. Part of this analysis involves establishing a direct connection
between the geometry of the curve graph and the combinatorics of
hyperplanes in these cubical models.*
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