10 papers · 1 filter
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…
A short proof of a conjecture of Aougab-Huang
Jonah Gaster
In response to Sanki-Vadnere, we present a short proof of the following theorem: a pair of simple curves on a hyperbolic surface whose complementary regions are disks has length at…
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…
Combinatorics of -Farey graphs
Jonah Gaster, Miguel Lopez, Emily Rexer +2
With an eye towards studying curve systems on low-complexity surfaces, we introduce and analyze the -Farey graphs and , two natural va…
Computing discrete equivariant harmonic maps
Jonah Gaster, Brice Loustau, Léonard Monsaingeon
We present effective methods to compute equivariant harmonic maps from the universal cover of a surface into a nonpositively curved space. By discretizing the theory appropriately,…