5 citations · 12 across the 9 of their papers we have counts for
11 papers
The distribution of critical graphs of Jenkins-Strebel differentials
Francisco Arana-Herrera, Aaron Calderon
By work of Jenkins and Strebel, given a Riemann surface X and a simple closed multi-curve on it, there exists a unique quadratic differential q on X whose horizontal foliation…
The shapes of complementary subsurfaces to simple closed hyperbolic multi-geodesics
Francisco Arana-Herrera, Aaron Calderon
Cutting a hyperbolic surface X along a simple closed multi-geodesic results in a hyperbolic structure on the complementary subsurface. We study the distribution of the shapes of th…
Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow
Aaron Calderon, James Farre
We extend Mirzakhani's conjugacy between the earthquake and horocycle flows to a bijection, demonstrating conjugacies between these flows on all strata and exhibiting an abundance…
Framed mapping class groups and the monodromy of strata of Abelian differentials
Aaron Calderon, Nick Salter
This paper investigates the relationship between strata of abelian differentials and various mapping class groups afforded by means of the topological monodromy representation. Bui…
Relative homological representations of framed mapping class groups
Aaron Calderon, Nick Salter
Let be a surface with either boundary or marked points, equipped with an arbitrary framing. In this note we determine the action of the associated "framed mapping class group"…
Higher spin mapping class groups and strata of Abelian differentials over Teichm{ü}ller space
Aaron Calderon, Nick Salter
For , we give a complete classification of the connected components of strata of abelian differentials over Teichmüller space, establishing an analogue of Kontsevich and Z…
Connected components of strata of Abelian differentials over Teichmüller space
Aaron Calderon
This paper describes connected components of the strata of holomorphic abelian differentials on marked Riemann surfaces with prescribed degrees of zeros. Unlike the case for unmark…
How to hear the shape of a billiard table
Aaron Calderon, Solly Coles, Diana Davis +2
The bounce spectrum of a polygonal billiard table is the collection of all bi-infinite sequences of edge labels corresponding to billiard trajectories on the table. We give methods…
Generalized bipyramids and hyperbolic volumes of alternating -uniform tiling links
Colin Adams, Aaron Calderon, Nathaniel Mayer
We present explicit geometric decompositions of the hyperbolic complements of alternating -uniform tiling links, which are alternating links whose projection graphs are -unif…
Generalized bipyramids and hyperbolic volumes of tiling links
Colin Adams, Aaron Calderon, Xinyi Jiang +4
We present explicit geometric decompositions of the complement of tiling links, which are alternating links whose projection graphs are uniform tilings of the 2-sphere, the Euclide…
Volume and Determinant Densities of Hyperbolic Rational Links
Colin Adams, Aaron Calderon, Xinyi Jiang +4
The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determin…