I am mostly interested in quantum topology. The following is a non-exhaustive list of my interests:
Quantum knot invariants, especially those which arise from ribbon categories/algebras.
Tangle categories.
Finite type invariants and the Kontsevich invariant.
Tensor categories
Modular categories, modular functors, modular operads.
Factorisation homology, skein categories.
XC-tangles and universal invariants
Jorge Becerra
Minimal generating sets of rotational Reidemeister moves
Jorge Becerra, Kevin van Helden
A refined functorial universal tangle invariant
Jorge Becerra
Strictification and non-strictification of monoidal categories
Jorge Becerra
On Bar-Natan - van der Veen's perturbed Gaussians
Jorge Becerra
Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 118, 46 (2024)
Jorge Becerra
European J. Combin. 124 (2025), Paper No. 104086.
An Introduction to Knot Homology Theories
Jorge Becerra
TEMat monográficos, 2 (2021): Proceedings of the 3rd BYMAT Conference, pp. 11-14. ISSN: 2660-6003.
Ascenso y Descenso Finito, Infinito y Torcido [Finite, Infinite and Twisted Ascent and Descent]
Jorge Becerra, Jesús MF Castillo
Universal quantum knot invariants (PhD thesis, supervised by Roland van der Veen). This thesis focuses on two knot invariants: the universal invariant subject to a ribbon Hopf algebra —that dominates the Reshetikhin-Turaev invariants coming from the representation theory of the Hopf algebra— and the Kontsevich invariant —which is universal among finte type invariants—. More precisely, Gaussian calculus techniques developed by Bar-Natan and van der Veen are exploited to study a family of knot polynomial invariants that determines the universal invariant subject to a specific algebra, and to investigate how the most elementary polynomial of this collection is closely related to the so-called 2-loop polynomial of the knot, an invariant that encodes a certain part of its Kontsevich invariant.
K-theory with Reality (Master's thesis, supervised by Lennart Meier). This was mainly a project on (Equivariant) Stable Homotopy Theory, where we specially studied the spectra KO and K of real and complex K-theory, and the Z/2-spectrum KR of K-theory with Reality, arising from considering vector bundles with an anti-linear involution in the category of Z/2-spaces.
Theory of Relativity (Bachelor's thesis, supervised by Juan A. Navarro). It is a beautiful walk from Classical Mechanics to General Relativity, written from the point of view of pseudo-Riemannian geometry. The goal was to describe in a mathematical way the structures of Classical Mechanics (Galilean Spacetime, Newtonian Gravitation) and the Theory of Relativity (Minkowski Spacetime, Newton-Cartan Gravitation). An overview in English can be found here).