Research interests

I am interested in low dimensional topology, that is, the topology of knots, 3-manifolds and 4-manifolds. More precisely, I am working in a field called quantum topology, which relates low dimensional topology to the theory of tensor categories, Hopf algebras and quantum groups. 

I'm particularly interested in non-semisimple tensor categories and the invariants of knots and 3-manifolds obtained from them (e.g. ADO, CGP). I'm trying to show that these invariants contain deep geometric information of knots, and much clearer than their semisimple counterparts (Jones, HOMFLY, WRT).

Previous to my PhD, I did research in the theory of combinatorial Hopf algebras (here is my master thesis).

Publications/Preprints

6. (with R. van der Veen). Genus bounds from unrolled quantum groups at roots of unity. arXiv:2312.02070 (2023).

5. (with R. van der Veen). Genus bounds for twisted quantum invariants, arXiv:2211.15010 (2022). To appear in J. Eur. Math. Soc. (JEMS).

4. Twisted Kuperberg invariants and Reidemeister torsion via twisted Drinfeld doubles. arXiv:2201.13382. Trans. Amer. Math. Soc. (2024).

3. Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion. arXiv:1911.02925. Algebr. Geom. Topol. (2022).

2. Kuperberg invariants for balanced sutured 3-manifolds. arXiv:1904.05786. Can. J. Math. (2021).

1. (with L. F. Préville-Ratelle and M. Ronco). A simplicial complex splitting associativity, arXiv:1906.02834. J. Pure Appl. Algebra (2020).

Teaching

6. Spring 2024: M312 -  Calculus IV. 

5. Spring 2023: M311 -  Calculus III. (2 sections)

4. Fall 2022: M211 - Calculus I.

3. Spring 2022: M212 - Calculus II. (2 sections)

2. Fall 2021: M301 - Linear Algebra and Applications.

1. Spring 2021: M119 - A Brief survey of calculus 1.

Other

In 2022, with Colleen Delaney, we organized an online seminar in quantum topology. Click HERE for more.