Taras Panov (Lomonosov Moscow State University, Moscow)
Geometric structures on moment-angle manifolds.
Moment-angle complexes are spaces acted on by a torus and parametrised by finite simplicial complexes. They are central objects in toric topology, and currently are gaining much interest in the homotopy theory. Due the their combinatorial origins, moment-angle complexes also find applications in combinatorial geometry and commutative algebra. Moment-angle complexes corresponding to simplicial subdivision of spheres are topological manifolds, and those corresponding to simplicial polytopes admit smooth realisations as intersection of Hermitian quadrics in Cm.
After an introductory part describing the construction and the topology of moment-angle complexes, we shall concentrate on several interesting geometric properties of moment-angle manifolds, emphasising complex-analytic, symplectic and Lagrangian aspects.
Different parts of this talk are based on joint works with Victor Buchstaber, Andrei Mironov, Yuri Ustinovsky and Mikhail Verbitsky.