Research

How does geometry interact with complexity? This question, applied in various contexts, motivates much of my recent research and future research goals.

A recent project is about properties of arithmetic lattices in higher rank symmetric spaces. I use an explicit family of representations of the hyperbolic 3-manifold vol3 to explore the relationship between different measures of complexity, and exhibit behavior which is unique to the higher rank context.

I also study outer automorphisms of free groups, and in particular the stretch factors of outer automorphisms. I'm interested in how stretch factors of train track maps are influenced by the symmetry of the graph they take place on.

Publications and Preprints

A hyperbolic free-by-cyclic group determined by its finite quotients. To appear in Glasgow Mathematical Journal. (with N. Andrew, R. A. Lyman, and C. Pfaff)
Latent symmetry of graphs and stretch factors in Out(Fr). To appear in Groups, Geometry, And Dynamics.
Non-uniform lattices of large systole containing a fixed 3-manifold group. To appear in Algebraic and Geometric Topology. (accompanying mathematica file)
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)

Upcoming Talks

Feb. 28, 2025: Highway CA-17 Groups, Geometry, and Topology Seminar, UC Santa Cruz
March 6 - 8, 2025: 58th Spring Topology and Dynamics Conference, Geometric Group Theory Session, (virtual)
May 3 - 4, 2025: AMS Spring Western Sectional, Special Session on Topological and Geometric Structures on 3-Manifolds, Cal Poly SLO

Conferences and Travel

AMS Fall Western Sectional, UC Riverside (2024) Talk
Moving to higher rank: from hyperbolic to Anosov, Cetraro, Italy (2024)
Symposium for Women and Gender Minorities in Southern California, Pomona College (2024) Talk
Texas Geometry and Topology Conference, Rice University (2023) Lightning Talk
Women in Groups, Geometry, and Dynamics, Ashton, Idaho (2023)
ICERM Dynamics, Rigidity, and Arithmetic in Hyperbolic Geometry (2023)
UC Riverside Geometric Group Theory Workshop(2023)
USTARS, University of Washington (2023) Poster Presented

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