Cluster Algebras and Integrable Dynamics
Research Group Gekhtman
June 15 - August 15, 2011
Organizers: Michael Gekhtman, Mikhail Z. Shapiro, Serge Tabachnikov, Alek Vainshtein
This project was devoted to connections between cluster algebras and integrable systems. Cluster algebras were introduced by Fomin and Zelevbinsky originally to study total positivity and dual canonical bases for semisimple algebraic groups. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker relations, Somos sequences and Hirota equations to name just a few examples). The rapid development of the cluster algebra theory revealed relations between cluster algebras and Grassmanians, quiver representations, generalized associahedra, Teichmüller theory, Poisson geometry and many other branches of mathematics.