On Mirzakhani's twist torus conjecture
Aaron Calderon, James Farre

TL;DR
This paper investigates Mirzakhani's conjecture on the statistical distribution of twist tori in hyperbolic surface moduli space, demonstrating equidistribution for some families and singularity for others.
Contribution
It proves Mirzakhani's conjecture for specific families of twist tori and identifies multiple expanding families with distinct limiting distributions.
Findings
Certain twist tori equidistribute to Lebesgue measure
Other families have mutually singular limiting distributions
Results advance understanding of hyperbolic surface moduli space
Abstract
We address a conjecture of Mirzakhani about the statistical behavior of certain expanding families of ``twist tori'' in the moduli space of hyperbolic surfaces, showing that they equidistribute to a certain Lebesgue-class measure along almost all sequences. We also identify a number of other expanding families of twist tori whose limiting distributions are mutually singular to Lebesgue.
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Taxonomy
TopicsMathematics and Applications · Mathematical Dynamics and Fractals · Advanced Combinatorial Mathematics
