 Office: Center for Math & Computing 217
 Phone: 507 222 4360
 Email: hwong@carleton.edu
 Profile
 Connections
Introduction
Within mathematics, my specialty is in quantum topology. My research focuses on lowdimensional manifolds (knots, surfaces, and 3dimensional 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
Grants
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.
Publications

SO(3) quantum invariants are dense in C, Mathematical Proceedings of the Cambridge Philo sophical Society, Volume 148 (2), March 2010, pp 28995.

Quantum invariants can provide sharp Heegaard genus bounds, Osaka Journal of Mathemat ics, Volume 48 (3), September 2011, pp709718.

Joint with Nathan Dunfield, Quantum invariants of random Heegaard splittings, Algebraic & Geometric Topology, Volume 11, 2011, pp 21912205.

Joint with Francis Bonahon, Quantum traces for representations of surface groups in SL2, Geometry & Topology, Volume 15 (3), 2011, pp15691615.

Joint with Francis Bonahon, Kauffman brackets, character varieties, and triangulations of surfaces, AMS Contemporary Mathematics Series: Conference Proceedings of JacoFest, Volume 560, 2011, pp17919.
Personal Interests
Courses Taught This Year
 MATH 400: Integrative Exercise (Winter 2017)
 MATH 321: Real Analysis I (Winter 2017)
 MATH 400: Integrative Exercise (Spring 2017)
 MATH 236: Mathematical Structures (Spring 2017)