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.