Quantum integrable systems and TQFT

The project will investigate the construction of 2D topological quantum field theories (TQFT) from quantum integrable systems. The former are described in terms of Frobenius algebras, while the latter are given in terms of non-cocommutative Hopf algebras, so-called Yang-Baxter algebras which are defined in terms of solutions to the quantum Yang-Baxter equation. The Bethe ansatz, a technique used to diagonalise the Hamiltonian of the quantum integrable system, leads to a set of nonlinear equations describing a 2D TQFT.