Tenure-track talk

Résumé

Cluster algebras are combinatorial objects which naturally appear is very different contexts. We will begin with examples of occurrences of particular relations characteristic of cluster algebras. Then we will concentrate on one of these examples: the Baxter relation. This example will allows us to shift the focus to representation theory, after a brief detour by mathematical physics. The Baxter relation will be the key to explain our results and will lead us to talk about quantum groups, a category O of representations and other research interests. Ultimately, we will formulate a quantized version of this relation, via quantum cluster algebras.