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 (Pl├╝cker 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, Teichm├╝ller theory, Poisson geometry and many other branches of mathematics.