**Title:** Rough similarity, rigidity and the Manhattan Curve for metrics on

hyperbolic groups

**Speaker:** Steve Cantrell – The University of Chicago

**Abstract: **Consider a hyperbolic group equipped with two hyperbolic metrics

that are left invariant and are quasi-isometric to a word metric. A

natural question to ask is: when are these metrics roughly similar, i.e.

when are they within bounded distance after scaling by a positive

constant? In this talk we’ll discuss rigidity statements that characterize

rough similarity in terms of the properties of the so-called Manhattan

Curve. We’ll see how to study this curve using a blend of ideas coming

from ergodic theory and geometric group theory. This is based on joint

work with Ryokichi Tanaka.

**Zoom link:** https://osu.zoom.us/j/98033590349

**Meeting ID:** 980 3359 0349

**Password:** Mixing

**Recorded Talk:** https://osu.zoom.us/rec/play/oojIKeNTtJYj2_BDzTMoq_B838qwHXhn_iL8nILR-obhxHVOVdSq9i-yd1-KTAT3QgRolQBWdTVY5Nx_.tCVmCXOuKzaXbsN_?continueMode=true&_x_zm_rtaid=Vd768-G5T-qQzFi8nIZqcw.1619131951571.08574cec3bd38c984e60711df5327a21&_x_zm_rhtaid=146