I am a mathematician working in the area of quantum topology, especially its relationships with hyperbolic geometry and non-quantum topology. I am also very interested in applications of topology to the sciences.
BA, Pomona College. PhD, Yale University.
Awards and Affiliations
von Neumann Fellow, Institute for Advanced Study 2017-18.
National Science Foundation Grants
Standard Grant, RUI: Knots in Three-Dimensional Manifolds: Quantum Topology, Hyperbolic Geometry, and Applications (DMS-1906323), 2019-2022.
Standard Grant, RUI: Skeins on Surfaces (DMS-1510453 and DMS-1841221), 2015-2019.
Standard Grant, RUI: Relating Quantum and Classical Topology and Geometry (DMS-11522850), 2011-2016.
Project NeXT Fellow (green dot), Mathematical Association of America
Prize Teaching Award, Yale University
Research and Publications
(with Erica Flapan and Adam He) Topological descriptions of protein folding. Proceedings of the National Academy of Sciences, 116 (2019), no.19, 9360-9369.
(with Jennifer Franko Vasquez and Zhenghan Wang) Qubit representations of the braid groups from generalized Yang-Baxter matrices. Quantum Information Processing, Volume 15, Number 7 (2016), 3035-3042.
(with Francis Bonahon) Representations of the Kauffman bracket skein algebra I: Invariants and miraculous cancellations. Inventiones Mathematicae, Volume 204, Number 1 (2016), 195-243.
(with Francis Bonahon) The Witten-Reshetikhin-Turaev representation of the Kauffman bracket skein algebra. Proceedings of the American Mathematical Society, Volume 144, Number 6 (2016), 2711-2724.
(with Martin Bobb, Stephen Kennedy and Dylan Peifer) The Kauffman bracket arc algebra is finitely generated. Journal of Knot Theory and its Ramifications, Volume 25, Number 6 (2016), 1650034, 14pp.
(with Francis Bonahon) Quantum traces for representations of surface groups in SL2. Geometry & Topology, Volume 15, Number 3 (2011), 1569-1615.
(with Nathan Dunfield) Quantum invariants of random Heegaard splittings. Algebraic & Geometric Topology, Volume 11, Number 4 (2011), 2191-2205.
SO(3) quantum invariants are dense in C. Mathematical Proceedings of the Cambridge Philosophical Society, Volume 148, Number 2 (2010), 289-295.