My current research interests are in quantum algebra and quantum topology. More specifically, I study the non-semisimple representation theory of quantum groups at a root of unity. The quantum invariants of knots and three-manifolds in this setting are related to classical topological invariants, such as the Alexander polynomial. One motivation for my research is to give new perspectives on classical topology using quantum topological methods.

In my most recent work, I have constructed a non-abelian generalization of the Alexander polynomial from higher rank quantum groups and studied the representation-theoretic aspects surrounding them. I have shown that the two-variable sl3 invariant can detect mutation.

Here is the list of my publications and pre-prints:

7. A Generalization of the Alexander Polynomial from Higher Rank Quantum Groups
(submitted) Preprint available at: arxiv.org/abs/2008.06983

6. Seifert-Torres Type Formulas for the Alexander Polynomial from Quantum sl2
(submitted) Preprint available at: arxiv.org/abs/1911.00646

5. Verma Modules for Restricted Quantum Groups at a Fourth Root of Unity
(submitted) Preprint available at: arxiv.org/abs/1911.00641

4. Consequences of omitting spin-orbit partner configurations for B(E2) values and quadrupole moments in nuclei
(with L. Zamick, Y. Y. Sharon, S. J. Q. Robinson) Phys. Rev. C 91, 064321 (2015)

3. Scissors mode from a different perspective
(with L. Zamick) Phys. Rev. C 91, 054310 (2015)

2. Wave functions of the Q · Q interaction in terms of unitary 9-j coefficients
(with L. Zamick) Phys. Rev. C 91, 034331 (2015)

1. J = 0, T = 1 pairing-interaction selection rules
(with L. Zamick) Phys. Rev. C 91, 014304 (2015)