Helen Wong, Ph.D.
Department
Biography
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.
Education
BA, Pomona College. PhD, Yale University.
Awards and Affiliations
Simons Fellow in Mathematics, Simons Foundation, 2021-22.
Joan and Joseph Birman Fellowship, American Mathematical Society, 2021-22.
von Neumann Fellow, Institute for Advanced Study 2017-18.
National Science Foundation Grants
Standard Grant, RUI: Pure and Applied Knot Theory (DMS-2305414), 2023-2026.
Standard Grant, RUI: Knots in Three-Dimensional Manifolds: Quantum Topology, Hyperbolic Geometry, and Applications (DMS-1906323), 2019-2023.
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
Fulbright Research Award, Budapest Semesters in Mathematics
Research and Publications
(with Han-bom Moon) Consequences of the compatibility of skein algebra and cluster algebra on surfaces. New York Journal of Mathematics, Volume 30 (2024), 1648--1682.
(with Erica Flapan and Alireza Mashaghi) A tile modle of circuit topology for self-entangled biopoolymers. Scientific Reports, Volume 13, 8889 (2023).
(with Han-bom Moon) On the Poisson Structure of the Roger-Yang Kauffman bracket arc algebra. Quantum Topology, Volume 12, Issue 2 (2021), 265-308.
(with Shawn Cui, Kevin Tian, Jennifer Franko Vasquez, Zhenghan Wang) The search for leakage-free, entangling Fibonacci braiding gates. Journal of Physics A: Mathematical and Theoretical, Volume 52, Number 45 (2019) 455301
(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 Francis Bonahon) Representations of the Kauffman bracket skein algebra I: Invariants and miraculous cancellations. Inventiones Mathematicae, Volume 204, Number 1 (2016), 195-243.
(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) 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.