Solitons, Riemannian Geometry, Spectral Theory Educational Tools

9704613诺维科夫这个项目涉及分析、拓扑学/几何学和应用数学。将研究流体动力系统的哈密顿理论和精确可解的薛定谔算子。所使用的技术包括孤子，非线性波动理论中的渐近方法，Kac-Moody类型李代数，拓扑量子场理论，以及低维薛定谔算符频谱理论的非标准对称性。哈密顿系统是由许多无摩擦运动的粒子组成的系统，由一个复杂的微分方程组控制。哈密顿理论通过首先观察系统的总能量来简化这些微分方程，并经常揭示系统中隐藏的对称性。动力系统模拟自然界中的各种现象，如水波和天气系统。

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.