I study geometric group theory and geometric topology. My research focuses on outer automorphisms of free groups and mapping class groups of surfaces, including those of infinite type. A central theme of my work is understanding stretch factors—numerical invariants that measure dynamical complexity.

Publications and Preprints

Every weak Perron number is an end-periodic stretch factor (with Marissa Loving and Chenxi Wu). Arxiv: pdf

Given any weak Perron number λ, we construct an end-periodic homeomorphism f : Σ → Σ with Handel-Miller stretch factor equal to λ where Σ is a connected infinite-type surface with finitely many ends all accumulated by genus.

A hyperbolic free-by-cyclic group determined by its finite quotients. Glasgow Mathematical Journal. (with Naomi Andrew, Robbie A. Lyman, and Catherine Pfaff) Arxiv: pdf

We show that the group ⟨a,b,c,t:at=b,bt=c,ct=c⁢a−1⟩ is profinitely rigid amongst free-by-cyclic groups, providing the first example of a hyperbolic free-by-cyclic group with this property.

Latent symmetry of graphs and stretch factors in Out(Fr). Groups, Geometry, and Dynamics. (2025) Arxiv: pdf

Every irreducible outer automorphism of the free group of rank r is topologically represented by an irreducible train track map f : Γ → Γ for some graph Γ of rank r. Moreover, f can always be written as a composition of “folds” and a graph isomorphism. We give a lower bound on the stretch factor of an irreducible outer automorphism in terms of the number of folds of f and the number of edges in Γ. In the case that f is periodic on the vertex set of Γ, we show a precise notion of the latent symmetry of Γ gives a lower bound on the number of folds required. We use this notion of latent symmetry to classify all possible irreducible single fold train track maps.

Low complexity among principal fully irreducible elements of Out(F3). To appear in Algebraic and Geometric Topology. (with N. Andrew, R. A. Lyman, and C. Pfaff) Arxiv: pdf

We find the shortest realized stretch factor for a fully irreducible φ ∈ Out(F3) and show that it is realized by a “principal” fully irreducible element. We also show that it is the only principal fully irreducible outer automorphism in any rank produced by a single fold.

Non-uniform lattices of large systole containing a fixed 3-manifold group. Algebraic and Geometric Topology. (2025). accompanying mathematica file. Arxiv: pdf

Let d ≥ 2 be a square free integer and Q( √ d) a totally real quadratic field over Q. We show there exists an arithmetic lattice L in SL(8, R) with entries in the ring of integers of Q( √ d) and a sequence of lattices Λn commensurable to L such that the systole of the locally symmetric finite volume manifold Λn\SL(8, R)/SO(8) goes to infinity as n → ∞, yet every Λn contains the same hyperbolic 3-manifold group Π, a finite index subgroup of the arithmetic hyperbolic 3-manifold vol3. Notably, such an example does not exist in rank one, so this is a feature unique to higher rank lattices.