7 papers
Symplectic Tiling Billiards on Complete Affine Tori
Charles Daly, Fabian Lander
In 2023, Richard Schwartz introduced a new dynamical system which is a marriage of two types of familiar billiards, tiling billiards and symplectic billiards. In this paper we inve…
Asymptotics of the Meandering Number of a Cyclic Permutation
Charles Daly, Diaaeldin Taha
A cyclic meander is an embedded oriented loop in the plane intersecting a fixed infinite line, or circle, transversely in a linearly ordered set of points. By keeping track of…
Minimal Faithful Representations of Split Extensions by Abelian Groups
Charles Daly, Justin Kingsnorth
Every finite group admits a representation which is 'most efficient' in the sense that the representation is faithful and the dimension is minimal. We call such representations min…
Projective Rigidity of Once-Punctured Torus Bundles via the Twisted Alexander Polynomial
Charles Daly
In this paper we provide a means of certifying infinitesimal projective rigidity relative to the cusp for hyperbolic once punctured torus bundles in terms of twisted Alexander poly…
Computer Assisted Projective Rigidity
Charles Daly
In this paper we provide a computer assisted proof that about two thousand surgeries far away from the ideal point in the hyperbolic Dehn filling space of the figure-eight knot com…
Closed Affine Manifolds with an Invariant Line
Charles Daly
A closed affine manifold is a closed manifold with coordinate patches into affine space whose transition maps are restrictions of affine automorphisms. Such a structure gives rise…
Algebraic k-systems of curves
Charles Daly, Jonah Gaster, Max Lahn +2
A collection of simple closed curves on an orientable surface is an algebraic -system if the algebraic intersection number is equal to in absolu…