I'm a PhD student at the University of Chicago. My advisor is Benson Farb. I will be graduating this year.
My interests include Teichmüller theory,character varieties, and geometric group theory.
Papers and Works in progress:
- Algebraic entropy and the action of mapping class groups on character varieties (To appear in "Advances in Mathematics")
We extend the definition of algebraic entropy to endomorphisms of affine varieties. We then calculate the algebraic entropy of the action of elements of mapping class groups on various character varieties, and show that it is equal to a quantity we call the spectral radius, a generalization of the dilatation of a Pseudo-Anosov mapping class. Our calculations are compatible with all known calculations of the topological entropy of this action. - Translation surfaces with finite Veech groups (Submitted)
We show that every finite subgroup of
can be realized as the Veech group of some translation surface.
- Simple closed curves, word length, and nilpotent quotients of free groups (joint work with Khalid Bou-Rabee)
We consider the fundamental group π of a surface of finite type equipped with the infinite generating set consisting of all simple closed curves. We show that every nilpotent quotient of π has finite diameter with respect to the word metric given by this set. This is in contrast with a result of Danny Calegari that shows that π has infinite diameter with respect to this set. Furthermore, we give a general criterion for a finitely generated group equipped with a generating set to have this property.
- Metric distortion in the Schottky locus (In progress)
We compare two metrics on the moduli space of Riemann surfaces - the Teichmüller metric and the metric pulled back from the moduli space of principally polarized abelian varieties via the period map. We show that the metric distortion between these metrics is arbitrarily high.