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.
Modular categories, modular functors, modular operads.
Factorisation homology, skein categories.
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
La Gaceta de la RSME, Vol. 21, Nº 3, 2018, pages 497-516.
Work in progress:
A Hopf-algebraic construction of the 2-loop polynomial of genus one knots.
On the naturality of the universal tangle invariant.
Classification of lax-TQFTs in dimensions 1 and 2.
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).