Laboratory for Geometrical Methods in Mathematical Physics

• We have computed correlation numbers of Louisville minimal gravitation from Douglas structural equation
• Our team has researched Baker-Ahiezer discrete modules over a ring of difference operators
• Invariants have been calculated for symplectic field theory defining quantum integrable system
• An axiomatic approach has been developed to symplectic field theory
• Commuting operators have been produced by quantization of hamiltonians of Hopf hierarchy. Potential of a disc in symplectic field theory has been calculated
• Our neat has studied integrable hierarchies of topological type in zero power approximation for quantum cohomologies of torous Fano manifolds.
• We have described the structure of Poisson-Lee group of dressing transforms of the Darboux-Egorov system.
• We have studied nonlinerar cinematic equation describing propagation of concentration waves in dispersed bubble fluids.
• We have proposed differential conservation laws approximating the initial integro-differential equation. On the basis of these laws we have completed quantitative computations of wave propagation demonstrating possibility of kinetic tripping of distribution function.
• Mathematical provisions have been developed for a nonlinear acoustic tomograph (new generation). First such tomographs have been manufactured.
• We have developed a theory of isomonodromic deformation of nonlinear differential operators of infinite order.
• General type weak singularities have been classified to solve quazilinear Hamiltonian partial differential equation

Implemented results of research: We have developed software for computation and visualization of modularized theta-functions. The software allows to work with Whitham asymptotics of higher orders of evolutionary partial derivative equation

Education and career development:

• We have developed a lecture course for masters «Geomethric methods of mathematical physics», the course has been read at the Faculty of Physics and Mathermatics of the Moscow State University
• 2 doctoral dissertations and 7 candidate dissertations have been defendeed
• 6 national scientific summer schools for geomethrical methods for mathematical phyisics for undergraduates of final years and postgraduates

Organizational and structural changes:

A computer classroom is operating that is equipped for visualization of computational processes of mathematical physics