String Theory Journal Club

The Yang-Baxter and the pentagon equation serve as important equations in mathematical physics. They appear in two equally significant versions, the operator and the set-theoretical one. In this talk, we focus on the set-theoretic versions of both equations, where their solutions are known as Yang-Baxter maps and pentagon maps, respectively. First, we recall Yang-Baxter maps of a specific type (quadrirational maps) and show their connection to discrete integrable systems. Then, we propose a classification scheme for quadrirational solutions of the pentagon equation. That is, we give a full list of representatives of quadrirational maps on $\mathbb{CP}^1 \times \mathbb{CP}^1$ that satisfy the pentagon equation, modulo an equivalence relation. Finally, we demonstrate how Yang-Baxter maps can be derived from quadrirational pentagon maps.