Vortrag: "Operators on Hilbert space, algebraic geometry and algebraic topology"

Abstract:
With many structures from differential or algebraic geometry one can canonically associate algebras of operators on Hilbert space. These algebras can then be analyzed using tools from functional analysis but, more importantly,  also from algebraic topology. The most relevant tool from algebraic topology here is the cohomology theory given by topological K-theory, in the sense of Atiyah-Hirzebruch, and its generalizations. We illustrate these connections by a very concrete and elementary example motivated by so called toric varieties.