Profesor asistente
Departamento de Matemática
Facultad de Ciencias Físicas y Matemáticas (CFM)
Universidad de Concepción, Chile
Contacto: dlopezn (at) udec.cl
I defended my PhD in 2020 at Université de Paris, IMJ-PRG. Here is my PhD thesis. Then I was a postdoc at Indiana University (Bloomington) from 2021-2024.
Sierra Velluda, Bío-Bío, Chile
I am interested in low dimensional topology, that is, the topology of knots, 3-manifolds and 4-manifolds. More precisely, I a work 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, LG, CGP). The main goal of my research (so far) is 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).
11. (with C. Anghel and R. van der Veen). The top coefficient of the Links-Gould invariant is Murasugi-sum multiplicative. arXiv:2610.09354.
10. (with R. van der Veen). Top coefficients of ADO invariants are Murasugi-sum multiplicative. arXiv:2610.08638.
9. (with S. Garoufalidis). Genus bounds for knot polynomials of Lie superalgebras. arXiv:2607.11735.
8. (with R. van der Veen). A plumbing-multiplicative function from the Links-Gould invariant. arXiv:2502.12899. Slides (MCA).
7. (with R. van der Veen). Non-semisimple sl_2 quantum invariants of fibred links. Adv. Math. (2025).
arXiv:2407.15561. Videos: Tsinghua, BIRS-CMO.
6. (with R. van der Veen). Genus bounds from unrolled quantum groups at roots of unity. J. London Math. Soc. (2025). arXiv:2312.02070.
5. (with R. van der Veen). Genus bounds for twisted quantum invariants. To appear in J. Eur. Math. Soc. (JEMS). arXiv:2211.15010. Slides and video (K-OS). A poster.
4. Twisted Kuperberg invariants and Reidemeister torsion via twisted Drinfeld doubles. Trans. Amer. Math. Soc. (2024). arXiv:2201.13382. Video (Purdue).
3. Twisting Kuperberg invariants via Fox calculus and Reidemeister torsion. Algebr. Geom. Topol. (2022). arXiv:1911.02925.
2. Kuperberg invariants for balanced sutured 3-manifolds. Can. J. Math. (2021). arXiv:1904.05786. A poster.
1. (with L. F. Préville-Ratelle and M. Ronco). A simplicial complex splitting associativity. J. Pure Appl. Algebra (2020). arXiv:1906.02834
1. Notas cursillo posgrado UdeC (Octubre 2024).
In 2022, with Colleen Delaney, we organized an online seminar in quantum topology. Click HERE for more.