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math.GR2026
Groups Generated by Root Unipotents: Higher-rank and rank-one
Yanlong Hao
For , let \[ Γ(Q)=\langle E_{ij}(q_{ij}):i\neq j\rangle \] be the subgroup of generated by elementary matrices with nonzero rational param…
math.GR2024
On trace set of hyperbolic surfaces and a conjecture of Sarnak and Schmutz
Yanlong Hao
In this paper, we investigate the trace set of a Fuchsian lattice. There are two results of this paper: the first is that for a non-uniform lattice, we prove Scmutz's conjecture: t…
math.GR2022
Groups that (do not) act isometrically on hyperbolic spaces
Yanlong Hao
In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on so…