On the correspondence between root systems and cluster algebras

One of the first remarkable results in the structure theory of cluster algebras of finite type is their classification by root systems. Since its discovery by Fomin and Zelevinsky, many more surprising connections between cluster algebras and root systems have appeared. In this talk, I will give an overview of old connections, mention new connections, and propose a geometric explanation for these connections. This is partly based on joint work with Jiang-Hua Lu, available at arxiv: 2503.11391.

For information about the Richard P. Stanley Seminar in Combinatorics, visit… https://math.mit.edu/combin/