Our Laboratory

The Laboratory of Topology and Dynamics was created within the framework of the grant of the Government of Russia (contract No. 14.Y26.31.0025) under the direction of the leading scientist professor Louis Hirsch Kauffman from the University of Illinois at Chicago.

Research areas:

1) Construction of new invariants for classical nodes, knotoids, and virtual knots. Establishing of decomposition theorems for knots, graphs, and braids in 3-manifolds. Finding linear representations for generalizations of braid groups. Finding of new categorizations for invariants of virtual links and the studying of homotopy types associated with categorizations. Calculation of volumes and other geometric invariants of hyperbolic knots, manifolds, and orbifolds.

2) Studying of geometry and dynamics in classical and quantum magnetic fields on surfaces and three-dimensional manifolds. Development of new geometric methods for solving problems in mathematical physics.

3) Investigation of the connections between the low-dimensional topology and theoretical physics based on Artin braid groups and Clifford algebras in the case of Majorana fermions. The studying of the topological properties of DNA and folding of proteins through the use of knotoids for study curves with open ends. Description of topological properties of configuration spaces for some robotics systems.