4 citations · 16 across the 14 of their papers we have counts for
23 papers
From arcs to curves: quadratic growth of 1-systems
Tarik Aougab, Jonah Gaster
We show that a collection of simple closed curves pairwise intersecting at most once on an orientable surface of Euler characteristic has at most curves. Up…
Twist numbers on hyperbolic once-punctured tori
Jonah Gaster
On a hyperbolic surface homeomorphic to a torus with a puncture, each oriented simple geodesic inherits a well-defined relative twist number in , given by the ratio to its h…
Combinatorially random curves on surfaces
Tarik Aougab, Jonah Gaster
We study topological properties of random closed curves on an orientable surface of negative Euler characteristic. Letting denote the conjugacy class of the st…
Boundary slopes for the Markov ordering on relatively prime pairs
Jonah Gaster
Following McShane, we employ the stable norm on the homology of the modular torus to investigate the Markov ordering on the set of relatively prime integer pairs with $q\ge…
Curves on the torus intersecting at most k times
Tarik Aougab, Jonah Gaster
We show that any set of distinct homotopy classes of simple closed curves on the torus that pairwise intersect at most times has size . Prior to this wo…
The sum of Lagrange numbers
Jonah Gaster, Brice Loustau
Combining McShane's identity on a hyperbolic punctured torus with Schmutz's work on the Markov Uniqueness Conjecture (MUC), we find that MUC is equivalent to the identity \begin{eq…