Shalom’s conjecture on affine actions of hyperbolic groups on l2

Establish that every hyperbolic group admits a proper, uniformly Lipschitz affine action on the Hilbert space l2.

Background

The authors obtain uniformly Lipschitz affine actions for hyperbolic groups on l1 and position their result within a broader program motivated by Shalom’s conjecture regarding actions on l2.

They explicitly reference Shalom’s conjecture as an open problem through the citations [Che01, Open Problem 14] and [Now15, Conjecture 35].