Beijing-Moscow Mathematics Colloquium (online)
摘要（Abstract）
The talk is devoted to the theory of topological insulators - a new and actively developing direction in solid state physics. To find a new topological object one have to look for the appropiate topological invariants and systems for which these invariants are non-trivial. The topological insulators are characterized by having wide energy gap stable for small deformations. A nice example is given by the quantum Hall spin insulator. It is a two-dimensional insulator invariant under the time reversal. It is characterized by the non-trivial topological Z_2-invariant introduced by Kane and Mele.
In our talk we consider the topological insulators invariant under time reversal. In the first part we present the physical basics of their theory while the second part deals with the mathematical aspects. These aspects are closely related to K-theory and non-commutative geometry.
主讲人简介（Bio）
Prof. Armen Glebovich Sergeev is a leading scientific researcher of the department of complex analysis in Steklov Mathematical Institute and a professor in Mechanical and Mathematical department of Moscow State University. He Got Ph. D in Moscow State University in 1975 and Doctor of Sciences in Steklov Mathematical Institute at Moscow in 1989. He is a foreign member of Armenian Academy of Sciences, member of the board of Moscow Mathematical Society and a member of Executive Committee of European Mathematical Society. He is the Chief-editor of many mathematical journals and published 106 papers and is the author of 10 books. His Principal fields of research include Pseudoconvex polyhedral, Invariant domains of holomorphy, Geometric quantization, Twistor quantization, Seiberg-Witten equations, Pseudoholomorphic curves and Vortex equations. He has been the scientific advisors of many doctors. Together with Prof. Xiangyu Zhou, they have organized a series of Sino-Russia Joint mathematical conferences for many years which has promoted greatly the mathematical cooperation between two countries.
