67 citations · 177 across the 50 of their papers we have counts for
56 papers
On Pappus and Anosov Representations of the Modular Group
Richard Evan Schwartz
Let . Let be the space of discrete faithful representations of the modular group into ${\rm Isom\/}(X)$ which map the order generator to an isometr…
The Four Color Theorem meets Shapes of Polyhedra
Richard Evan Schwartz
We consider solutions to the -color problem for the vertices of sphere triangulations with degree sequence . We sort these solutions into combinatorial type…
The Optimal Twisted Paper Cylinder
Noah Montgomery, Richard Evan Schwartz
An embedded twisted paper cylinder of aspect ratio is a smooth isometric embedding of a flat cylinder into such that the images of the boundary components ar…
The Optimal Paper Moebius Band
Richard Evan Schwartz
In this paper we prove that a smooth embedded paper Moebius band must have aspect ratio greater than . We also prove that any sequence of smooth embedded paper Moebius ban…
Symplectic Tiling Billiards, Planar Linkages, and Hyperbolic Geometry
Richard Evan Schwartz
In this paper I will unite two games, symplectic billiards and tiling billiards. The new game is called symplectic tiling billiards. I will prove a result about periodic orbits of…
Divide and Conquer: A Distributed Approach to Five Point Energy Minimization
Richard Evan Schwartz
This work rigorously verifies the phase transition in 5-point energy minimization first observed by Melnyk-Knop-Smith in 1977. More precisely, we prove that there is a constant S =…