Mathematical Sciences Research Institute

Organized By: Sergey Fomin (University of Michigan), Bernhard Keller (Universit´e Paris VII, France), Bernard Leclerc (Universit´e de Caen, France), Alexander Vainshtein* (University of Haifa, Israel), Lauren Williams (University of California, Berkeley).

Cluster algebras were conceived in the Spring of 2000 as a tool for studying dual canonical bases and total positivity in semisimple
Lie groups. They are constructively defined commutative algebras with a distinguished set of generators (cluster variables) grouped into overlapping subsets (clusters) of fixed cardinality. Both the generators and the relations among them are not given from the outset, but are produced by an iterative process of successive mutations. Although this procedure appears counter-intuitive at first, it turns out to encode a surprisingly widespread range of phenomena, which might explain the explosive development of the subject in recent years. Cluster algebras provide a unifying algebraic/combinatorial framework for a wide variety of phenomena in diverse settings ranging from tropical calculus to Lie theory and from Poisson geometry to invariant theory.Possibly due to the fact that cluster-like structures were for quite some time implicit in many areas of mathematics, the field has exploded in recent years.

The program will focus on links between cluster algebras and other areas, such as: polyhedral combinatorics; triangulations of surfaces; Y, Q, and T-systems; additive categorification via quiver representations; quivers with potentials and Donaldson-Thomas invariants; Lie theory and monoidal categorification; Poisson geometry and Teichmueller theory.

Workshops for this Program:
Connections for women: commutative algebra and cluster algebras
Organizers: I.Peeva, I.Reiten, K.Smith, and L.Williams

Introductory workshop: commutative algebra and cluster algebras
Organizers: B.Keller, A.Vainshtein
Speakers: S.Fomin, D.Thurston, B.Leclerc, A.Vainshtein.

Cluster algebras in combinatorics, algebra, and geometry
Organizers: S.Fomin, A.King, B.Leclerc

Workshops for this Program:

Joint Introductory Workshop: Cluster Algebras and Commutative Algebra
August 27, 2012 to September 7, 2012

Questions about this program should be sent either by email to the Program Coordinator or by regular mail to:

Cluster Algebras Mathematical Sciences Research Institute 17 Gauss Way, Berkeley, CA 94720-5070. USA

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