[Binghamton Geometry Topology Seminar] GT Seminar: Prayagdeep Parija speaks today

[Jose Roman Aranda Cuevas]

Hi everyone,

Today we are pleased to have Prayagdeep Parija from UW Milwaukee speaking
about random quotients. As usual, the talk will be at 2:50 pm.

The speaker will deliver the talk remotely, and we'll project it in WH
100E. In case you can't make it and would like to join remotely, you can
join at the link:

https://binghamton.zoom.us/j/2060048595

As usual, there will be a lunch gathering and meeting at noon on Thursday
outside WH100E. See you there!

Best,
Cary and Roman

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Title: Random quotients of hyperbolic groups and Property (T)

Abstract: What does a random quotient of a group look like? Gromov
introduced the density model of quotients of free groups. The density
parameter d measures the rate of exponential growth of the number of
relators compared to the size of the Cayley ball. Using this model, he
proved that for d<1/2 a random quotient of a free group is non-elementary
hyperbolic. Ollivier extended Gromov's result to show that for d<1/2 a
random quotient of even a non-elementary hyperbolic group is non-elementary
hyperbolic.

Żuk/Kotowski-Kotowski proved that for d>1/3 a typical quotient of a free
group has Property (T). We show that for 1/3<d<1/2 (in a closely related
density model) a random quotient of a non-elementary hyperbolic group is
non-elementary hyperbolic and has Property-(T).

This provides an answer to a question of Gromov (and Ollivier)
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