[Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Matt Durham

[Cary Malkiewich]

Hi everyone,

This week we are pleased to have Matt Durham (UC Riverside) speaking about
some fancy new properties of mapping class groups and Teichmuller space,
title and abstract below. This will be an *in person* talk, on Thursday at
2:50pm in WH 100E.

Matt will be coming down from Cornell, hopefully by noon, so our plan is to
go to lunch with him at 12pm. Meet just outside WH 100E if you would like
to join!

Best,
Cary

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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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