Abstract:
In this talk we consider mathematical problems arising in the theory of
topological unsulators. These are the solid bodies having the broad energy gap
stable under small deformations which motivates the application of topological methods
for their study.
A key role in the theory of topological insulators is played by the study of their
symmetry groups, going back to Kitaev, who proposed a classification of
topological objects in the solid state physics based on the representation theory
of Clifford algebras. In our talk we pay a special attention to the topological insulators
invariant under time reversion. From the mathematical point of view their invextigation
reduces to the study of topological spaces, provided with involution, and quaternion
vector bundles over them.
