Laboratory for the Study of Quantum Topology
This laboratory was established as part of a scientific research project supported with a monetary grant awarded by the Government of the Russian Federation under a grant competition designed to provide governmental support to scientific research projects implemented under the supervision of the world's leading scientists at Russian institutions of higher learning (Resolution of the RF Government No.220 of April 9, 2010).
Grant Agreement No.:
Name of the institution of higher learning:
Chelyabinsk State University
Fields of scientific research:
To perform research in the field of quantum and small-scale topology, including applications in contiguous areas of mathematics.
Project implementation outputs:
The project team has developed a number of new methods of creating and calculating quantum invariants of manifolds and nodes, put together tables of nodes within a thickened tor that can be used in the development of bi-periodic textile structures. The scientists have determined precise values for an infinite series of three-dimensional hyperbolic manifolds, which substantially expands the existing catalogues. The project has helped identify conditions for unique solvability of special systems of differential equations that are used in the theory of multiphase environment and have multiple applications. The scientists have introduced a new class of Hurwitz figures required for creation of a broad class of new infinitely dimensional topological field theories. They have put together a new class of generating functions for Hurwitz figures that has turned out to be associated with integrating systems, matrix models and other research fields of modern mathematical physics.
Full Name: Touraev Vladimir Georgiyevich
Link to the scientist's profile
Academic degree and title:
PhD in Physics and Mathematics, Professor
Boucher Professor at the Indiana State University Bloomington (USA)
Head of the Laboratory for the Study of Quantum Topology at the Chelyabinsk State University (Russia)
Field of scientific interests:
Topology and mathematical physics: topology of manifolds in algebra, quantum topology, theory of quantum groups, topological quantum field theory.
The leading scientist is one of the cofounders of quantum topology whose achievements include the following:
- precise formulation of the topological quantum field theory via surgery and theory of quantum groups;
- development of the first quantum invariants (Reshetikhin – Tourayev invariants);
- development of the topological quantum field theory that mathematically implements the Ponzanom – Rege three-dimensional gravitation model (Tourayev – Viro theory);
- Establishment of the Laboratory for the Study of Quantum Groups and Quantum Topology at the Institute of High Mathematical Research in Strasbourg (France), which has by now turned out a number of outstanding researchers. The laboratory successfully operates to this day.
CNRS Silver Medal, France (2004).