I am a postdoc at Indiana University, Bloomington. I defended my PhD in 2020 at Université de Paris, IMJ-PRG, under the supervision of Christian Blanchet. Here is my PhD thesis and my CV. You can contact me at dlopezne (at) indiana.edu.

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. 

Currently, my research is oriented towards exploiting the flexibility of non-semisimple tensor categories to capture topological information of knots beyond their isomorphism class.

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


5. Genus bounds for twisted quantum invariants, joint with Roland van der Veen. arXiv:2211.15010 (2022).

4. Twisted Kuperberg invariants and Reidemeister torsion via twisted Drinfeld doubles. arXiv:2201.13382 (2022).

3. Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion. arXiv:1911.02925 (2019). Algebraic and Geometric Topology.

2. Kuperberg invariants for balanced sutured 3-manifolds. arXiv:1904.05786 (2019). Canadian Journal of Mathematics.

1. A simplicial complex splitting associativity, joint with L. F. Préville-Ratelle and M. Ronco. arXiv:1906.02834 (2019). Journal of Pure and Applied Algebra.


5. Spring 2023: M311 -  Calculus III.

4. Fall 2022: M211 - Calculus I.

3. Spring 2022: M212 - Calculus II.

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

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


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