12 citations · 15 across the 11 of their papers we have counts for
14 papers
Finiteness of closed arithmetic hyperbolic surface bundles
Tam Cheetham-West, Homin Lee, Nicholas Miller
For each , we show that there are finitely many cyclic commensurability classes of closed, fibered arithmetic hyperbolic -manifolds with genus fiber. More generally,…
A note on an effective characterization of covers with an application to higher rank representations
Tarik Aougab, Max Lahn, Marissa Loving +1
In this note we prove an effective characterization of when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of…
Azumaya algebras and once-punctured torus bundles
Nicholas Miller
Recent work of Chinburg, Reid, and Stover has shown that certain arithmetic and algebro-geometric properties of the character variety of a hyperbolic knot complement in the 3-spher…
Shifts maps are not type-preserving
Carolyn Abbott, Nicholas Miller, Priyam Patel
For a surface of sufficient complexity, Dehn twists act elliptically on the arc, curve, and relative arc graph of . We show that composing a Dehn twist with a shift map resu…
Unmarked simple length spectral rigidity for covers
Tarik Aougab, Max Lahn, Marissa Loving +1
We prove that every closed orientable surface S of negative Euler characteristic admits a pair of finite-degree covers which are length isospectral over S but generically not simpl…
Infinite-type loxodromic isometries of the relative arc graph
Carolyn R. Abbott, Nicholas Miller, Priyam Patel
An infinite-type surface is of type if it has an isolated puncture and admits shift maps. This includes all infinite-type surfaces with an isolated puncture o…
Arithmeticity, superrigidity and totally geodesic submanifolds of complex hyperbolic manifolds
Uri Bader, David Fisher, Nicholas Miller +1
For , we prove that a finite volume complex hyperbolic -manifold containing infinitely many maximal properly immersed totally geodesic submanifolds of dimension at leas…
Arithmeticity, Superrigidity, and Totally Geodesic Submanifolds
Uri Bader, David Fisher, Nick Miller +1
Let be a lattice in . We prove that if the associated locally symmetric space contains infinitely many maximal totally geodesic subspaces of dimension at l…
On the genus of congruence surfaces from maximal orders
Eric Albers, Nicholas Miller
In this paper, we investigate a question of Breuillard and Reid concerning which genera can be obtained by closed congruence surfaces. Specifically, we study a smaller set of objec…
Effective virtual and residual properties of some arithmetic hyperbolic 3-manifolds
Jason DeBlois, Nicholas Miller, Priyam Patel
We give an effective upper bound, for certain arithmetic hyperbolic 3-manifold groups obtained from a quadratic form construction, on the minimal index of a subgroup that embeds in…
Finiteness of Maximal Geodesic Submanifolds in Hyperbolic Hybrids
David Fisher, Jean-François Lafont, Nicholas Miller +1
We show that large classes of non-arithmetic hyperbolic -manifolds, including the hybrids introduced by Gromov and Piatetski-Shapiro and many of their generalizations, have only…
Areas of totally geodesic surfaces of hyperbolic 3-orbifolds
Benjamin Linowitz, D. B. McReynolds, Nicholas Miller
The geodesic length spectrum of a complete, finite volume, hyperbolic 3-orbifold M is a fundamental invariant of the topology of M via Mostow-Prasad Rigidity. Motivated by this, th…
Arithmetic Progressions in the Primitive Length Spectrum
Nicholas Miller
In this article, we prove that every arithmetic locally symmetric orbifold of classical type without Euclidean or compact factors has arbitrarily long arithmetic progressions in it…
Locally Equivalent Correspondences
Benjamin Linowitz, D. B. McReynolds, Nicholas Miller
Given a pair of number fields with isomorphic rings of adeles, we construct bijections between objects associated to the pair. For instance we construct an isomorphism of Brauer gr…