Khrystyna Serhiyenko (University of Kentucky) will conduct an online mini-course on cluster algebras. The course is intended for Ukrainian students, both undergraduate and graduate and may be suitable for advanced high schoolers. Lectures will be given in English.

Cluster algebras are a class of commutative rings with a good combinatorial structure. They were introduced by Fomin and Zelevinsky in 2002 to study total positivity and the canonical basis in Lie theory, but quickly developed into a very active research area with surprising connections to many other branches of mathematics and physics.

In this course, we will introduce cluster algebras and study their basic properties, including positivity and the Laurent phenomenon. We will also discuss two important classes of cluster algebras, namely those arising from surface triangulations and Grassmannian coordinate rings.

Khrystyna Serhiyenko is currently an assistant professor at University of Kentucky, where she is a member of the discrete math group. During 2015-2018, she was an NSF postdoc at University of California, Berkeley, and during 2018-2019 she was a lecturer there. She received her PhD from the University of Connecticut in 2015.

Her research interests include representation theory of associative algebras, cluster algebras, and related combinatorics. Recently, jointly with Sherman-Bennett and Williams, Khrystyna Serhiyenko solved a well-known folklore conjecture that the coordinate rings of Schubert varieties can be identified with cluster algebras.

"There are no specific prerequisites, I will define/explain all the necessary background, and there will be a lot of combinatorics that should be easily accessible to students."