30 citations · 83 across the 14 of their papers we have counts for
16 papers
Parabolic-preserving deformations of cusped hyperbolic lattices
Samuel A. Ballas, Julien Paupert, Pierre Will
We study deformations of non-cocompact lattices of into and . A necessary condition for these deformations to remain discrete and f…
Geometric Perspective on Concentration Phenomena in Frame Theory
Samuel A. Ballas, Ferhat Karabatman, Tom Needham
Parseval and equal-norm frames play a fundamental role in frame theory and signal processing. It is known that a random frame, with unit vectors drawn independently from the unifor…
On the existence of Parseval frames for vector bundles
Samuel A. Ballas, Tom Needham, Clayton Shonkwiler
Frames in finite-dimensional vector spaces are spanning sets of vectors which provide redundant representations of signals. The Parseval frames are particularly useful and importan…
Tame and relatively elliptic -structures on the thrice-punctured sphere
Samuel A. Ballas, Philip L. Bowers, Alex Casella +1
Suppose a relatively elliptic representation of the fundamental group of the thrice-punctured sphere is given. We prove that all projective structures on with holonomy…
The Moduli Space of Marked Generalized Cusps in Real Projective Manifolds
Samuel A. Ballas, Daryl Cooper, Arielle Leitner
In this paper, a generalized cusp is a properly convex manifold with strictly convex boundary that is diffeomorphic to where is a closed Euclidean manifo…
Gluing equations for real projective structures on 3-manifolds
Samuel A. Ballas, Alex Casella
Given an orientable ideally triangulated --manifold , we define a system of real valued equations and inequalities whose solutions can be used to construct projective structu…
Thin subgroups isomorphic to Gromov--Piatetski-Shapiro lattices
Samuel A. Ballas
In this paper we produce many examples of thin subgroups of special linear groups that are isomorphic to the fundamental groups of non-arithmetic hyperbolic manifolds. Specifically…
Constructing thin subgroups of SL(n+1,R) via bending
Samuel Ballas, D. D. Long
In this paper we use techniques from convex projective geometry to produce many new examples of thin subgroups of lattices in special linear groups that are isomorphic to the funda…
Constructing convex projective 3-manifolds with generalized cusps
Samuel A Ballas
We prove that non-compact finite volume hyperbolic 3-manifolds that satisfy a mild cohomological condition (infinitesimal rigidity) admit a family of properly convex deformations o…
Generalized Cusps in Real Projective Manifolds: Classification
Samuel A. Ballas, Daryl Cooper, Arielle Leitner
A generalized cusp is diffeomorphic to times a closed Euclidean manifold. Geometrically is the quotient of a properly convex domain by a lattice, , in one o…
Rank 1 deformations of non-cocompact hyperbolic lattices
Samuel A. Ballas, Julien Paupert, Pierre Will
Let be a negatively curved symmetric space and a non-cocompact lattice in . We show that small, parabolic-preserving deformations of into the isometry gro…
Properly convex bending of hyperbolic manifolds
Samuel A. Ballas, Ludovic Marquis
In this paper we show that bending a finite volume hyperbolic -manifold along a totally geodesic hypersurface results in a properly convex projective structure on wi…
Convex projective structures on non-hyperbolic three-manifolds
Samuel A. Ballas, Jeffrey Danciger, Gye-Seon Lee
Y. Benoist proved that if a closed three-manifold M admits an indecomposable convex real projective structure, then M is topologically the union along tori and Klein bottles of fin…
Constructing thin subgroups commensurable with the figure-eight knot group
Samuel A. Ballas, Darren Long
In this paper we find infinitely many lattices in each of which contains thin subgroups commensurable with the figure-eight knot group.
Finite Volume Properly Convex Deformations of the Figure-eight Knot
Samuel A. Ballas
In this paper we show that some open set of the representations of the fundamental group of figure-eight knot complement found in \cite{Ballas12a} are the holonomies of a family of…
Deformations of Non-Compact, Projective Manifolds
Samuel A. Ballas
In this paper, we demonstrate that the complete hyperbolic structure of various two-bridge knots and links cannot be deformed to an inequivalent strictly convex projective structur…