Every curve is a Teichmuller curve (2009)
Ellenberg, Jordan S., McReynolds, D. B.
We prove that every algebraic curve X defined over the algebraic closure of the rationals is birational over the complex numbers to a Teichmuller curve.
Bertrand's postulate and subgroup growth (2009)
Bou-Rabee, K., McReynolds, D. B.
In this article we investigate the L^1-norm of certain functions on groups called divisibility functions. Using these functions, their connection to residual finiteness, and integration theory on...
Asymptotic growth and least common multiples in groups (2009)
Bou-Rabee, K., McReynolds, D. B.
The goal of this article is to study the interplay between word and subgroup growth for finitely generated groups. We relate word and subgroup growth with norms of certain functions that arise in the...
The congruence subgroup problem for braid groups: Thurston's proof (2009)
In this article we present an unpublished proof of W. Thurston that pure braid groups have the congruence subgroup property.
Controlling manifold covers of orbifolds (2009)
In this article we prove a generalization of Selberg's lemma on the existence of torsion free, finite index subgroups of arithmetic groups. Some of the geometric applications are the resolution a...
The genus spectrum of a hyperbolic 3-manifold (2009)
McReynolds, D. B., Reid, Alan W.
In this article we study the spectrum of totally geodesic surfaces of a finite volume hyperbolic 3-manifold. We show that for arithmetic hyperbolic 3-manifolds that contain a totally geodesic...
Graphs of subgroups of free groups (2009)
Louder, Larsen, McReynolds, D. B.
We construct an efficient model for graphs of finitely generated subgroups of free groups. Using this we give a very short proof of Dicks's reformulation of the strengthened Hanna Neumann Conjecture...
Cusps of Hilbert modular varieties (2008)
Motivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifold M to be...
Arithmetic lattices and weak spectral geometry (2007)
This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the...
Cusps of Hilbert modular varieties (2007)
Motivated by a question of Hirzebruch on the possible topological types of cusp cross-sections of Hilbert modular varieties, we give a necessary and sufficient condition for a manifold M to be...
Length and eigenvalue equivalence (2007)
C. J. Leininger, D. B. Mcreynolds, W. D. Neumann, A. W. Reid
Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace-Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent...
Length and Eigenvalue Equivalence (2007)
Leininger, C. J., McReynolds, D. B., Neumann, W. D., Reid, A. W.
Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace–Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent...
Cusps of arithmetic orbifolds (2006)
This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic $n$-orbifolds. We give a smooth classification of these submanifolds and analyze their induced...
Cusps of arithmetic orbifolds (2006)
This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic $n$--orbifolds. We give a smooth classification of these submanifolds and analyze their induced...
Constructing isospectral manifolds (2006)
In this article we construct nonisometric, isospectral manifolds modelled on semisimple Lie groups with finite center and no compact factors. Specifically, our two main results are the construction...
Arithmetic cusp shapes are dense (2006)
In this article we verify an orbifold version of a conjecture of Nimershiem from 1998. Namely, for every flat $n$-manifold $M$, we show that the set of similarity classes of flat metrics on $M$ which...
Length and eigenvalue equivalence (2006)
Leininger, Christopher J., McReynolds, D. B., Neumann, Walter D., Reid, Alan W.
Two Riemannian manifolds are called eigenvalue equivalent when their sets of eigenvalues of the Laplace-Beltrami operator are equal (ignoring multiplicities). They are (primitive) length equivalent...
Finite subgroups of arithmetic lattices in U(2,1) (2006)
The principle result of this article is the determination of the possible finite subgroups of arithmetic lattices in U(2,1).
Separable subgroups of mapping class groups 1 Separable subgroups of mapping class groups (2006)
Christopher J. Leininger, D. B. Mcreynolds
We investigate separability questions for the mapping class group of a surface. While this group is not subgroup separable in general, we prove a large family of interesting subgroups are separable....
Separable subgroups of mapping class groups (2005)
Leininger, Christopher J., McReynolds, D. B.
We investigate the separability of several well known classes of subgroups of the mapping class group of a surface.
Peripheral separability and cusps of arithmetic hyperbolic orbifolds (2004)
For X = R, C, or H it is well known that cusp cross-sections of finite volume X-hyperbolic (n+1)-orbifolds are flat n-orbifolds or almost flat orbifolds modelled on the (2n+1)-dimensional Heisenberg...