Research

My research lies in non-commutative algebra, with connections to group theory and mathematical physics. A central theme of my work is the study of algebraic structures related to the Yang–Baxter equation and the Pentagon equation, together with their interactions with areas such as Hopf–Galois theory and the theory of skew braces.

Current research interests

My current work focuses on the interplay between set-theoretic solutions of the Pentagon equation and set-theoretic solutions of the Yang–Baxter equation. I am especially interested in understanding this interplay also beyond the category of sets, in more general contexts.

Research themes

  • set-theoretic solutions of the Yang–Baxter equation
  • set-theoretic solutions of the Pentagon equation
  • skew braces, trusses, and related algebraic structures
  • regular subgroups of the holomorph and Hopf–Galois-type applications
  • computational aspects, especially using GAP

Selected recent work

  1. Colazzo, I., Okniński, J., & Van Antwerpen, A. (2026). Bijective solutions to the Pentagon Equation. accepted for publication in Selecta Mathematica.
  2. Colazzo, I., & Janssens, G. (2026). On set-theoretic solutions of pentagon equation and positive basis Hopf algebras. arXiv.
  3. Colazzo, I., Jespers, E., Kubat, Ł., Van Antwerpen, A., & Verwimp, C. (2023). Finite Idempotent Set-Theoretic Solutions of the Yang–Baxter Equation. International Mathematics Research Notices, rnad183. https://doi.org/10.1093/imrn/rnad183

Further information