- Date
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Thursday 19 December 2024, 11.30 - 12.30
- Abstract
- Classifying matrix solutions to the Yang-Baxter equation is a problem noted for both its simplicity and a dearth of effective strategies. Recent work with Martin classifying charge conserving solutions to the Yang-Baxter in all dimensions has inspired us to look at the general problem afresh (or possibly poisoned us with hubris). In particular the categorical perspective suggests that there may be other families of solutions that are amenable to classification. In work with Martin and Torzewska, we have begun excavating the structure and properties of the category $MonFun(B,Mat)$ of strong monoidal functors from the braid category $B$ to the category $Ma$t of matrices, to see if it will expose a new vein of classification ore. I will discuss our progress so far, with an eye towards putting past success into this broader context and deciding if it can be repeated or if it was just a flash in the pan.
