arXiv subjects

Joseph Wells

Publications and source records attributed to Joseph Wells.

4 recordsLinked to original sources

arXiv2025

High dimensional hyperbolic Coxeter groups that virtually fiber

This paper provides an iterative procedure for constructing hyperbolic Coxeter groups that virtually fiber over $\mathbb{Z}$ that is flexible enough to yield infinitely many isomorphism classes in each virtual cohomological dimension (vcd) $n\geq 2$. Our procedure combines results of Jankiewicz, Norin, and Wise with a generalization of a construction due to Osajda involving a new simplicial thickening process. We also give a topological argument showing that the vcd of the right-angled Coxeter groups produced by our construction increases by exactly one with each iteration, guaranteeing that our process produces examples of every vcd.

math.GT↗

arXiv2020

Fisher-Rao distance on the covariance cone

The Fisher-Rao geodesic distance on the statistical manifold consisting of zero-mean p-dimensional multivariate Gaussians appears without proof in several places (such as Steven Smith's "Covariance, Subspace, and Intrinsic Cramer-Rao Bounds"). In this paper, we give a proof using basic Riemannian geometry.

math.ST↗

arXiv2019

Hybrid lattices and thin subgroups of Picard modular groups

We consider a certain hybridization construction which produces a subgroup of ${\rm PU}(n,1)$ from a pair of lattices in ${\rm PU}(n-1,1)$. Among the Picard modular groups ${\rm PU}(2,1,\mathcal{O}_d)$, we show that the hybrid of pairs of Fuchsian subgroups ${\rm PU}(1,1,\mathcal{O}_d)$ is a lattice when $d=1$ and $d=7$, and a geometrically infinite thin subgroup when $d=3$, that is an infinite-index subgroup with the same Zariski-closure as the full lattice.

math.GT↗

arXiv2019

Non-arithmetic hybrid lattices in $\mathrm{PU}(2,1)$

We explore hybrid subgroups of certain non-arithmetic lattices in $\mathrm{PU}(2,1)$. We show that all of Mostow's lattices are virtually hybrids; moreover, we show that some of these non-arithmetic lattices are hybrids of two non-commensurable arithmetic lattices in $\mathrm{PU}(1,1)$.

math.GT↗