Five Glimpses of Cluster Algebras

Michael Gekhtman, Notre Dame University

Abstract: Cluster algebras were introduced by Fomin and Zelevinsky just over 20 years ago and have since found exciting applications in many areas including algebraic geometry, representation theory, integrable systems and theoretical physics.  I will use examples to explain the definition of a cluster algebra and then sketch several applications of the theory, including Somos-5 recursion, pentagram map and generalizations of Abel's pentagon identity. (Portions of this presentation will also be of interest to upper-level undergraduate students.)

Tea and refreshments available at 3:00 p.m. in the Assmus Conference Room (CU 212).