From cluster algebras to Higgs categorles

Speaker: Bernhard Keller

Venue: Lecture Hall 210, Haina Complex Building 2, Zijingang Campus

Abstract: Cluster algebras are certain commutative algebras invented by Fomin-Zelevinsky around the year 2000. Among them, we find the homogeneous coordinate algebras of Grassmannians, flag varieties and many other varieties of importance in representation theory and geometry. Fomin-Zelevinsky's motivations came from Lie theory and more precisely from the study of Lusztig's (dual) canonical bases which such algebras possess and from his related theory of total positivity. In this talk. we will briefly review the history of cluster algebras and their links to many other subjects including Lie theory, discrete dynamical systems, quiver representations, Donaldson-Thomas theory, mirror symmetry and symplectic topology.