Helen Wong




Contact Information


Department of Mathematics

Claremont McKenna College

850 Columbia Ave

Claremont, CA 91711


(909) 607-9922

hwong at-symbol (initials of college, three letters, sounds like see-em-see) dot edu


Office in Adams Hall Room 219



Academic Positions Held


Claremont McKenna College, Associate Professor, 2018-present.

Institute for Advanced Study, von Neumann Fellow, 2017-2018.

Carleton College, Assistant Professor 2009-2016, Associate Professor 2016-18.

Bowdoin College, Postdoctoral Teaching Fellow, 2007-2009.





Yale University, New Haven, CT.

PhD in Mathematics, 2007. 


Budapest Semesters in Mathematics, Hungary.

Fulbright Student Research Fellow, 1999-2000.


Pomona College, Claremont, CA.

BA in Mathematics, summa cum laude, 2000. 




Links to Professional Profiles

·      Faculty Profile at Claremont McKenna College

·      Profile on MathSciNet

·      Papers on the arXiv




Research Publications


v Low-dimensional Geometric Topology and Quantum Topology

(especially Kauffman bracket skein modules and algebras, polynomial invariants of links, quantum invariants of 3-manifolds, and their relationships to hyperbolic geometry and non-quantum topology)

1.    (with Han-bom Moon) On the Poisson Structure of the Roger-Yang Kauffman bracket arc algebra. In preparation.

2.     (with Francis Bonahon) Representations of the Kauffman bracket skein algebra III: closed surfaces and naturality.  Quantum Topology,  Volume 1, Issue 2 (2019), 325-398.

3.    (with Francis Bonahon) Representations of the Kauffman bracket skein algebra II: Punctured surfaces. Algebraic & Geometric Topology, Volume 17, Number 6 (2017), 3399--3434.

4.    (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.

5.    (with Martin Bobb, Stephen Kennedy and Dylan Peifer)  Presentations of Kauffman bracket arc algebra for small surfaces.   Involve: A Journal of Mathematics, Volume 9, Number 4 (2016), 689-698.

6.    (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.

7.    (with Francis Bonahon) Representations of the Kauffman bracket skein algebra I: Invariants and miraculous cancellations. Inventiones Mathematicae, Volume 204, Number 1 (2016), 195-243.

8.    (with Francis Bonahon) Quantum traces for representations of surface groups in SL2.  Geometry & Topology, Volume 15, Number 3 (2011), 1569-1615.

9.     (with Francis Bonahon) Kauffman brackets, character varieties, and triangulations of surfaces.  Topology and geometry in dimension three (Proceedings of JacoFest), 179-194.   Contemporary Mathematics Series, Volume 560, American Mathematical Society, Providence, RI, 2011. 

10. (with Nathan Dunfield) Quantum invariants of random Heegaard splittings.  Algebraic & Geometric Topology, Volume 11, Number 4 (2011),  2191-2205.

11.Quantum invariants can provide sharp Heegaard genus bounds. Osaka Journal of Mathematics, Volume 48, Number 3 (2011), 709-718.

12. SO(3) quantum invariants are dense in C. Mathematical Proceedings of the Cambridge Philosophical Society, Volume 148, Number 2 (2010), 289-295. 

13. The SO(3) quantum invariants: their density and topological applications. Ph.D. thesis, Yale University, under the direction of Andrew Casson, 2007. 


v Applications of Topology and Geometry

(including Topological quantum computing, Knotting in DNA and proteins, Topological data analysis)

1.    (with Shawn Cui, Kevin Tian, Jennifer Franko Vasquez, Zhenghan Wang) The search for leakage-free, entangling Fibonacci braiding gates.   arXiv:104.01731.  Submitted and under review.

2.     (with Erica Flapan and Adam He) Topological descriptions of protein folding. Proceedings of the National Academy of Sciences, April 2019, 201808312; DOI: 10.1073/pnas.1808312116

3.     (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.

4.    (with Erica Flapan, Jeremy Grevet, Qi Li and Daisy Sun) Knotted and linked products of recombination on T(2,n)#T(2,m) substrates. Journal of the Korean Mathematics Society, Volume 51, Number 4 (2014), 817--836.



Books, Edited Volumes, and Selected Other Products


1.    (edited with Erica Flapan) Topology of Biopolymers.  Contemporary Mathematics Volume, American Mathematical Society. Expected to appear in 2020.

2.    Three entries in  A Concise Encyclopedia of Knot Theory, editors  C. Adams, E. Flapan, A. Heinrich, L. Kauffman, L. Ludwig, S. Nelson, CRC Press.  Expected to appear in 2020.

a.    (with Jozef Przytycki) Skein Modules

b.    (with Jozef Przytycki) Kauffman Bracket Skein Modules and Algebras

c.     Protein knots, links, and non-planar graphs.

3.    (with Erica Flapan and other members of the Park City Mathematics Institute Undergraduate Faculty Program) Knots, Molecules, and the Universe: An Introduction to Topology.  American Mathematical Society, 2015.

4.    Exhibitions of Mathematical Models

a.    (with library curator Margaret Pezalla-Granlund  and the students of Senior Seminar: Knot Theory) If It's Knot Theory, What Is It? Gould Library, Carleton College, Spring and Summer 2015.

b.    (with the students of Senior Seminar: Surfaces) Quilting, Copper, and Yarn: Math with Models. Gould Library, Carleton College, Fall 2011.

c.     (with museum curator Diana Tuite) Curating Across Disciplines: Intersections between Mathematics and Art. Becker Gallery, Bowdoin College Museum of Art,  Spring 2008.

5.    Contributions to the publications of the Girls' Angle: A Math Club for Girls, Boston.

a.    An Interview with Helen Wong. Girls' Angle Bulletin, Volume 3, Number 5, July 2010.

b.     Adding the Numbers from 1 to 100. Women in Mathematics Video Series.

c.     Summer Fun: Adding Up Numbers. Girls' Angle Bulletin, Volume 3, Number 5, July 2010.

6.     (with Anna Dragonova) Instructor's manual for J. Pommersheim, T. Marks, and E. Flapan,  Number Theory: A Lively Introduction with Proofs: Applications, and Stories, Wiley, 2010.




Selected Grants and Honors


·      Colby College Ninetta Runnals Speaker for Women in Mathematics, 2018.  

·      NSF DMS-1906323, RUI: Knots in Three-Dimensional Manifolds: Quantum Topology, Hyperbolic Geometry, and Applications, 2019-2022. 

·      NSF DMS-1510453, DMS-1841221, RUI: Skeins on Surfaces, 2015-2020.

·      NSF DMS-11522850, RUI: Relating Quantum and Classical Topology and Geometry, 2011-2016.

·      AWM Mentoring Travel Grant, 2010-11.

·      AWM Travel Grant, 2007.

·      MAA Project NExT Fellowship, Richard Good Fund, 2009-10 (Green Dot).

·      Yale University Prize Teaching Fellowship, 2007.

·      Pomona College Phi Beta Kappa, Barbara Sanford and Bertha Clendenen McCord Prizes in Music, 1999.