Research Interests
My research interests lie in the areas of Teichmüller theory, mapping class groups, and hyperbolic geometry. I am currently investigating how the coarse geometry of Teichmüller space relates to certain properties of quadratic differentials and to other aspects of Teichmüller dynamics. I am also interested in the connections between hyperbolic geometry and the largescale geometry of Teichmüller space.
My CV is available here.
Papers and Preprints
 Statistical hyperbolicity for harmonic measure, with Aitor Azemar and Vaibhav Gadre. Submitted, 13 pages. arXiv:1909.13811
Abstract: We consider harmonic measures that arise from random walks on the mapping class group determined by a probability distribution that has finite first moment with respect to the Teichmüller metric, and whose support generates a nonelementary subgroup. We prove that Teichmüller space with the Teichmüller metric is statistically hyperbolic for such a harmonic measure.

Singlecylinder squaretiled surfaces and the ubiquity of ratiooptimising pseudoAnosovs. Submitted, 39 pages. arXiv:1906.02016
Abstract: In every connected component of every stratum of Abelian differentials, we construct squaretiled surfaces with one vertical and one horizontal cylinder. We show that for all but the hyperelliptic components this can be achieved in the minimum number of squares necessary for a squaretiled surface in that stratum. For the hyperelliptic components, we show that the number of squares required is strictly greater and construct surfaces realising these bounds.
Using these surfaces, we demonstrate that pseudoAnosov homeomorphisms optimising the ratio of Teichmüller to curve graph translation length are, in a reasonable sense, ubiquitous in the connected components of strata of Abelian differentials. Finally, we present a further application to filling pairs on punctured surfaces by constructing filling pairs whose algebraic and geometric intersection numbers are equal.
 Minimally intersecting filling pairs on the punctured surface of genus two. Topology Appl. 254 (2019) 101106.
doi: 10.1016/j.topol.2018.12.011
Abstract: In this short note, we construct a minimally intersecting pair of simple closed curves that fill a genus 2 surface with an odd, at least 3, number of punctures. This finishes the determination of minimally intersecting filling pairs for all surfaces completing the work of AougabHuang and AougabTaylor.
Abstract: We consider harmonic measures that arise from random walks on the mapping class group determined by a probability distribution that has finite first moment with respect to the Teichmüller metric, and whose support generates a nonelementary subgroup. We prove that Teichmüller space with the Teichmüller metric is statistically hyperbolic for such a harmonic measure.
Abstract: In every connected component of every stratum of Abelian differentials, we construct squaretiled surfaces with one vertical and one horizontal cylinder. We show that for all but the hyperelliptic components this can be achieved in the minimum number of squares necessary for a squaretiled surface in that stratum. For the hyperelliptic components, we show that the number of squares required is strictly greater and construct surfaces realising these bounds.
Using these surfaces, we demonstrate that pseudoAnosov homeomorphisms optimising the ratio of Teichmüller to curve graph translation length are, in a reasonable sense, ubiquitous in the connected components of strata of Abelian differentials. Finally, we present a further application to filling pairs on punctured surfaces by constructing filling pairs whose algebraic and geometric intersection numbers are equal.
doi: 10.1016/j.topol.2018.12.011
Abstract: In this short note, we construct a minimally intersecting pair of simple closed curves that fill a genus 2 surface with an odd, at least 3, number of punctures. This finishes the determination of minimally intersecting filling pairs for all surfaces completing the work of AougabHuang and AougabTaylor.