9704613 Novikov This project lies in the interface of analysis, topology/geometry, and applied mathematics. Hamiltonian theory of hydrodynamical systems, and exactly solvable Schrodinger operators are to be investigated. The techniques to be used include solitons, asymptotic methods in nonlinear wave theory, Kac-Moody type Lie algebras, topological quantum field theories, and nonstandard symmetry for the spectral theory of low-dimensional Schrodinger operators. Hamiltonian systems are systems composed of many particles moving without friction and are governed by a complicated system of differential equations. Hamiltonian theory simplifies these differential equations by first looking at the total energy of the system and often reveals hidden symmetries in the system. Dynamical systems model various phenomena in nature such as water waves and weather systems.
