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Abstract: Topological insulators are the solid bodies having a broad energy gap stable under small deformations. This motivates the usage of topological methods for their study.
A key role in the theory of solid states is played by their symmetry groups. Kitaev has pointed out that there is a relation between the symmetries of solid bodies and Clifford algebras. According to this observation the quantization of topological insulators should reduce to the theory of irreducible representations of Clifford algebras.
The next important step was done by Kennedy and Zirnbauer who introduced the notion of pseudosymmetries. While the algebra of observables of a topological insulator is generated by Hamiltonians satisfying commutation relations with symmetry operators, the quantum obsrvables are given by the complex sstructures on the Nambu space satisfying anticommutation relations with pseudosymmetries. This correspondence determines the quantization of topological insulators.
Bio: Armen Glebovich Sergeev is an outstanding Russian mathematician whose interests include complex analysis and complex geometry of tubular domains, pseudoholomorphic curves, matrix domains of holomorphy, geometric quantization, Seiberg-Witten equations, vortex equations, infinite-dimensional Kähler manifolds and harmonic mappings of compact Riemann surfaces into Kähler manifolds. Besides, studies the universal Teichmüller space, which contains the classical Teichmüller spaces of compact Riemann surfaces of finite genus as complex submanifolds.
Prof. Sergeev graduated from the Faculty of Mechanics and Mathematics of Moscow State University in 1971. Four years later, he defended his PhD thesis on the topic “Multidimensional factorization problem and multiplicative theory of hyperfunctions” being supervised by Prof. A. G. Kostyuchenko.
Since 1982, he has been working at the Steklov Mathematical Institute (MIAN), now being Deputy Director of the institute.
In 1989, Armen Sergeev became Doctor of Physical and Mathematical Sciences. He teaches at the Faculty of Mechanics and Mathematics, as a professor of the Department of Function Theory and Functional Analysis (1994).
Besides, Prof. Sergeev is a Member of the Board of the Moscow Mathematical Society (MMS), Editor of the MMS Proceedings, Deputy Editor-in-Chief of the journal “Izvestiya RAS. Mathematical Series”. Honorary Doctor of Heńań University (Heńań, China) and foreign Member of the National Academy of Sciences of the Republic of Armenia (2014).
