Publications and preprints

1. Periodic points of endperiodic maps. PDF. ArXiv link. Groups Geom. Dyn. (2025), published online first

   Abstract: Let g : L → L be an atoroidal, endperiodic map on an infinite type surface L with no boundary and finitely many ends, each of which is accumulated by genus. By work of Landry, Minsky, and Taylor, g is isotopic to a spun pseudo-Anosov map f. We show that spun pseudo-Anosov maps minimize the number of periodic points of period n for sufficiently high n over all maps in their homotopy class, strengthening a theorem of Landry, Minsky, and Taylor. We also show that the same theorem holds for atoroidal Handel--Miller maps when one only considers periodic points that lie in the intersection of the stable and unstable laminations. Furthermore, we show via example that spun-pseudo Anosov and Handel--Miller maps do not always minimize the number of periodic points of low period.

Work from undergraduate

1. Domains of Convergence for Polyhedral Packings. With Nooria Ahmed, William Ball, Emilie Rivkin, Dylan Torrance, Jake Viscusi, Runze Wang, Ian Whitehead, and S. Yang. ArXiv link.

   Abstract: Polyhedral circle packings are generalizations of the Apollonian packing. We develop the theory of the Apollonian group, Descartes quadratic form, and related objects for all polyhedral packings. We use these tools to determine the domain of absolute convergence of a generating function that can be associated to any polyhedral packing. This domain of convergence is the Tits cone for an infinite root system.

2. Appendix to Littlewood--Richardson rules from quivers for two-step flag varieties. With Linda Chen and Elana Kalashnikov. ArXiv link.

   Abstract: Let ⋀1 and ⋀2 be two symmetric function algebras in independent sets of variables. We define vector space bases of ⋀1⊗Z⋀2 coming from certain quivers, with vertex sets indexed by pairs of partitions. We use these vector space bases to give a positive tableau formula for Littlewood--Richardson coefficients for the product of Schubert polynomials with certain Schur polynomials in two-step flag varieties, in the spirit of the Remmel-Whitney rule for the product of two Schur polynomials in Grassmannians. This in particular covers the cases considered by the Pieri rule.