Pavlo Pylyavskyy (University of Minnesota) will teach an online mini-course on cluster algebras. All with algebraic and combinatorics interests are welcome to register. No specific prerequisite knowledge is expected.

Cluster algebras were discovered around the year 2000, and since then have become a big topic of research, with multiple applications in various areas of mathematics and physics. At the beginning however cluster algebras were met with some skepticism, people would ask: what can you prove using cluster algebras that we couldn't prove before? The first such thing was the conjecture of Zamolodchikov on periodicity of certain recursions, motivated by physics. I will talk about the setting of T-systems in which this happens, Zamolodchikov conjectures, Volkov's proof in a special case. Then I will move on to classification results and to generalization of periodicity called integrability. Parts of the course will be based on joint work with Pavel Galashin.