Low-dimensional topology and the Yang–Baxter equation (topYB)

International Joint Research Group (IJRG)

Chair: VUB • Co-chair: University of Leeds

About topYB

Low-dimensional topology and the Yang–Baxter equation (topYB) is an International Joint Research Group (IJRG) between Vrije Universiteit Brussel (VUB), Belgium and the University of Leeds (UK).

Mission. We aim to explore a discrete version of the celebrated Yang–Baxter equation, their algebraic structures and application to low-dimensional topology.

Apart from focusing on algebra and topology, we explore the intersection of these fields with other areas in pure mathematics, such as Hopf–Galois structures and Topological Quantum Field Theory. Additionally, we expand our research into computer science, particularly through constraint programming techniques to construct solutions with special properties and to facilitate interdisciplinary contributions.

Yang–Baxter structures Low-dimensional topology Hopf–Galois TQFT Constraint programming
Algebra School (June 2026) Meet the team

Governance & partners

Chair
Vrije Universiteit Brussel (VUB), Brussels (Belgium)
Co-chair
University of Leeds, Leeds (United Kingdom)
Contact persons
Leandro Vendramin (VUB) • Ilaria Colazzo (Leeds)

Research themes

Discrete / set-theoretic Yang–Baxter equation

We study discrete versions of the Yang–Baxter equation, their classifications, and the algebraic structures that arise from solutions.

Low-dimensional topology & invariants

We connect Yang–Baxter-type structures to knot theory and related low-dimensional topological constructions.

Hopf–Galois structures & algebra

We explore interactions with Hopf–Galois theory and related algebraic frameworks that encode symmetry and factorisation.

Topological Quantum Field Theory (TQFT)

We investigate links to quantum/topological field theories and the algebraic input needed to build and compare TQFT-style invariants.

Computational & constraint programming methods

We develop computational pipelines—especially constraint programming—to construct and search for solutions with prescribed properties.

Want to collaborate or propose a student/postdoc visit? See Contact.