Department of Mathematics

Seminar in Cluster algebras

  •  Alexander Vainshtein, Haifa University
  •  Cluster structures on SL_n and the Belavin-Drinfeld classification
  •  09/19/2022
  •  12:30 PM - 1:30 PM
  •  C304 Wells Hall
  •  Michael Shapiro (

Cluster structures were discovered by S. Fomin and A. Zelevinsky about twenty years ago and quickly found applications in various fields of mathematics and mathematical physics. In the latter, several advances were made in a study of classical and quantum integrable systems arising in the context of cluster structures. These systems "live" on Poisson-Lie groups and their Poisson homogeneous spaces, hence it is important to understand an interplay between cluster and Poisson structures on such objects. In this talk I will explain a construction of a family of (generalized) cluster structures in the algebra of regular functions on SL_n related to the Belavin-Drinfeld classification of Poisson-Lie structures on SL_n. Based on a joint work with M.~Gekhtman (Notre Dame) and M.~Shapiro (MSU).



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science