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Helen Wong

Helen Wong


Within mathematics, my specialty is in quantum topology.   My research focuses on low-dimensional manifolds (knots, surfaces, and 3-dimensional manifolds) and particularly the use of quantum invariants in order to distinguish them apart.  Although inspired by quantum physics and geometry, the quantum invariants can be calculated using only algebraic manipulations of pictures and diagrams.  In a sense, my research asks how, if at all, these pictures capture geometrical information.  I've led undergraduate projects that tie in directly with my research, and  I often introduce tidbits from my research in the courses I teach.  I'm also very interested in applications of topology, like in DNA biology or chemistry, and the use of visual tools to help us understand mathematics. 

Education & Professional History

Pomona College, BA; Yale University, PhD.

At Carleton since 2009.

Highlights & Recent Activity


National Science Foundation Grants, "Skeins on Surfaces" and “Relating quantum and classical topology and geometry”.    Carleton College Eugster and Class of ’49 Fellowships.  Association for Women in Mathematics Travel Grants.   Carleton College Visualization of the Liberal Arts Initiative Grant.   Mathematical Association of America Project NExT.  Fulbright Student Fellowship to Hungary.


  1. SO(3) quantum invariants are dense in C, Mathematical Proceedings of the Cambridge Philo- sophical Society, Volume 148 (2), March 2010, pp 289-95.

  2. Quantum invariants can provide sharp Heegaard genus bounds, Osaka Journal of Mathemat- ics, Volume 48 (3), September 2011, pp709-718.

  3. Joint with Nathan Dunfield, Quantum invariants of random Heegaard splittings, Algebraic & Geometric Topology, Volume 11, 2011, pp 2191-2205.

  4. Joint with Francis Bonahon, Quantum traces for representations of surface groups in SL2, Geometry & Topology, Volume 15 (3), 2011, pp1569-1615.

  5. Joint with Francis Bonahon, Kauffman brackets, character varieties, and triangulations of surfaces, AMS Contemporary Mathematics Series: Conference Proceedings of JacoFest, Volume 560, 2011, pp179-19. 




Courses Taught This Year

As Listed on Department Faculty Pages

Profile updated October 14, 2016

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