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
- Bijective solutions to the Pentagon Equation
Colazzo, Ilaria and Okniński, Jan and Van Antwerpen, Arne. Selecta Mathematica, 32, 93 (2026). - On set-theoretic solutions of pentagon equation and positive basis Hopf algebras
Colazzo, Ilaria and Janssens, Geoffrey (2026). - Finite Idempotent Set-Theoretic Solutions of the Yang–Baxter Equation
Colazzo, Ilaria and Jespers, Eric and Kubat, Łukasz and Van Antwerpen, Arne and Verwimp, Charlotte. International Mathematics Research Notices, rnad183 (2023).