Speaker
Description
After the discovery of quantum Hall effect and its topological explanation the mathematical methods based on the theory of $C^*$-algebras and their K-theory enter firmly into the arsenal of solid state physics.
A key role in the theory of solid states is played by their symmetry groups. It was Kitaev who has pointed out the relation between the symmetries of solid bodies and Clifford algebras.
In this talk we pay main attention to the class of solid bodies called the topological insulators. They are characterized by having a broad energy gap stable under small deformations. The algebras of observables of such solid bodies belong to the class of graded $C^*$-algebras for which there is a variant of K-theory proposed by Van Daele. It makes possible to define the topological invariants of insulators in K-theory terms.
