KTH/SU Mathematics Colloquium

November 12, 2008

Vladimir Fock, Moscow (ITEP) and Strasbourg

Cluster varieties - geometry and combinatorics

Cluster varieties are certain algebraic varieties completely defined by combinatorial data, namely by an arbitrary skew-symmetrizable integer-valued matrix. They can be constructed by gluing coordinate charts by explicit simple rational maps. They are provided with Poisson or degenerate symplectic structure, quantization, discrete symmetry group action preserving all these structures. Among the main examples of the cluster varieties are the Lie groups, Teichmueller spaces, moduli of flat connections on Riemann surfaces and many others group-related manifolds.