I'm a Gibbs assistant Professor at the Yale math department. I completed my Ph.D in 2011 at the University of Chicago, under the supervision of Benson Farb.

My fields of interest include geometric group theory, low dimensional topology, and dynamics – particularly the study of mapping class groups and the automorphism groups of free groups. My recent research has focused on developing a homological theory of laminations that arise from studying mapping classes and automorphisms of free groups.

## Papers and Works in progress:

- Algebraic entropy and the action of mapping class groups on character varieties
*(Advances in Mathematics 226(12): 3282-3296, 2011)*abstractWe 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)*abstractWe 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)**Pacific Journal of Mathematics 254(1): 67-72, 2011*abstractWe 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. - Linear representations of Aut(F_r) on the homology of representation varieties
*(Together with Yael Algom Kfir)(Submitted)*abstractLet G be a compact Lie group. We study the action of Aut(F_r) on the space H_*(G^r;\QQ). We compute both the image and kernel of this representation. We show that the Kernel is always the Torelli subgroup IA_r of Aut(F_r), and the image depends only on the rank of G. - Homological shadows of attracting laminations (Submitted)
*abstract*Given a free group $F_n$, a fully irreducible automorphism $f \in \aut$, and a generic element $x \in F_n$, the elements $f^k(x)$ converge in the appropriate sense to an object called an attracting lamination of $f$. When the action of $f$ on $\frac{F_n}{[F_n, F_n]}$ has finite order, we introduce a homological version of this convergence, in which the attracting object is a convex polytope with rational vertices, together with a measure supported at a point with algebraic coordinates.