11 citations · 43 across the 13 of their papers we have counts for
16 papers
Controlling ball progression in soccer
Catherine Pfaff, Emily Hunter, Haozhi Hong +4
In this paper, we examine how soccer players can use their spatial relationships to control parts of the field and safely move play up the field via chains of ``safe configurations…
Taking the High-Edge Route Through Outer Space in Rank 3
Damara Gagnier, Catherine Pfaff
Principal outer automorphisms were introduced in Algom-Kfir-Kapovich-Pfaff to emulate principal pseudo-Anosov surface homeomorphisms, i.e. those whose attracting and repelling inva…
Random trees in the boundary of Outer space
Ilya Kapovich, Joseph Maher, Catherine Pfaff +1
We prove that for the harmonic measure associated to a random walk on Out satisfying some mild conditions, a typical tree in the boundary of Outer space is trivalent and non…
Random outer automorphisms of free groups: Attracting trees and their singularity structures
Ilya Kapovich, Joseph Maher, Catherine Pfaff +1
We prove that a "random" free group outer automorphism is an ageometric fully irreducible outer automorphism whose ideal Whitehead graph is a union of triangles. In particular, we…
Counting conjugacy classes of fully irreducibles: double exponential growth
Ilya Kapovich, Catherine Pfaff
Inspired by results of Eskin and Mirzakhani counting closed geodesics of length in the moduli space of a fixed closed surface, we consider a similar question in the $Out(F_…
Stable Strata of Geodesics in Outer Space
Yael Algom-Kfir, Ilya Kapovich, Catherine Pfaff
In this paper we propose an Outer space analogue for the principal stratum of the unit tangent bundle to the Teichmüller space of a closed hyperbolic surface .…