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My interests lie in and around geometric topology and hyperbolic geometry. I particularly like hyperbolic 3-manifolds and am interested in quantitative refinements of the correspondence between their topology and geometry. I am also interested in various aspects of computational topology and geometric group theory.
"applied topology"
Stuff:
Magnetic geodesics, Hodge Laplacian eigenvalues, and isoperimetric inequalities, preprint.
Property (T) and Poincaré duality in dimension 3, preprint.
Degree one regulator bounds via stable systoles, note.
Filling 1-cycles, 2-cycle complexity, and torsion growth preprint.
Stretch laminations and hyperbolic Dehn surgery, preprint (this version is more recent than arXiv version).
Computing a link diagram from its exterior, with Nathan Dunfield and Malik Obeidin, Discrete & Computational Geometry, 71: 121–159, 2024.
An extended abstract for the paper above appeared in the proceedings of the Symposium on Computational Geometry (SoCG).
Stable isoperimetric ratios and the Hodge Laplacian of hyperbolic manifolds, Journal of Topology, 16: 588-633, 2023.
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