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My research investigates the structure of low-dimensional manifolds and the geometry of high-dimensional datasets.
My theoretical work focuses on 3- and 4-dimensional manifolds using tools such as Heegaard Floer homology.
My applied work studies graph partitions and the congressional redistricting problem from the perspective of fiber bundles, diffusion maps, and spectral geometry.
For an overview of some of my current projects, please see my Research Statement, some recent talk slides, and preprints below.
Papers
Papers
Applications of Fibered Diffusion Maps and Spectral Geometry to Ensembles of Graph Partitions and Congressional Redistricting Maps (with Duke Math+ Research Cohort Jenny Chan*, Peakay Clifford*, Greg Herschlag, Eileen Santana*, Felix Sesin*, Spencer Whitehead**, Leonard Yang*), Work in progress, Summer 2026. *denotes undergraduate students, **denotes a graduate student
Symmetries of immersed curves and correction terms (with Jonathan Hanselman and Marco Marengon), arXiv:2408.02857, 2024. Revision Requested at Algebraic & Geometric Topology. (61 pages).
Twisted Mazur pattern satellite knots & bordered Floer theory: Floer thickness, 3-genus, fiberedness, and the Cosmetic Surgery Conjecture (with Ina Petkova), Michigan Math. J., 73(2): 255--304, 2023.
A Floer homology invariant for 3-orbifolds via bordered Floer theory, arXiv:1808.09026, 2018.
G-corks and Heegaard Floer homology, J. Knot Theory Ramifications, 28 (2019), no. 12, 7 pp.
Turaev torsion invariants of 3-orbifolds, Geom. Dedicata 187 (2017), 179-197.
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