Math

Publications

• Determining hyperbolicity of compact orientable 3-manifolds with torus boundary, JoCG 11 (1), 125--136, 2020.
• Practical bounds for a Dehn parental test, Proc. Amer. Math. Soc. 147, 427--442, 2019.
• Tessellating the moduli space of strictly convex projective structures on the once-punctured torus, joint with Stephan Tillmann, Exp. Math. 28 (3), 369--384, 2019.

Preprints

• Hyperbolic 3-manifolds of low cusp volume, joint with David Gabai, G. Robert Meyerhoff, Nathaniel J. Thurston, and Andrew Yarmola, arXiv:2109.14570.
• On moduli spaces of convex projective structures on surfaces: outitude and cell-decomposition in Fock-Goncharov coordinates, joint with Robert Löwe, Dominic Tate, and Stephan Tillmann, arXiv:1911.04176.
• On the complexity of cusped non-hyperbolicity, joint with Neil Hoffman, arXiv:1907.01675.

Presentations

• Knot diagram recovery in exponential time, at the AMS 2020 Fall Southeastern Sectional Meeting Special Session on Interactions Between Algebra, Geometry and Topology in Low Dimensions
• On the complexity of cusped non-hyperbolicity, at the 2020 Joint Mathematics Meetings Special Session on Applications and Computations in Knot Theory
• Exceptional Dehn fillings and necklaces, at the 2016 Australian Mathematical Sciences Meeting Special Session on Topology

Projects

• An alternative algorithm for closed surfaces in knot complements, joint with Stephan Tillmann, Asem Wardak, and Abdul Zreika
• Representations of links in the three-sphere, joint with Neil Hoffman, Saul Schleimer, and Eric Sedgwick
• Rigorous length spectrum bounds for hyperbolic three-manifolds, joint with Matthias Görner, Neil Hoffman, and Maria Trnkova
• MOM-1.5s and hyperbolic three-manifolds with closed totally geodesic boundary, joint with Craig D. Hodgson and G. Robert Meyerhoff