Helen Wong

Topologist

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

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.

· Faculty Profile
at Claremont McKenna College

· Profile
on MathSciNet

· Papers on the arXiv

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 SL_{2}. *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.

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.

· 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.