Mathematical Sciences: Topology, Geometry, and Physics

三名研究人员将研究以下领域的问题： 几何偏微分方程，数学物理， 和动力系统。 一个人将继续调查 几何方面的Atiyah-Singer指数定理和 量子场论与低维的关系 topology. 第二个将继续进行调查， 调和映射方程及其与Poisson-Lie的联系 结构和量子群。 她还将调查 杨-米尔斯泛函的维数大于4。 第三 研究人员将研究周期轨道的结类型， 洛伦兹吸引子。 三名调查员将继续进行涉及 微分方程拓扑学和数学物理学 微分方程将一个或多个变量的变化率 相对于彼此或相对于时间的变量。 拓扑学是对形状的数学研究。 这两个领域 在数学物理学中有很长的使用历史。

Three investigators will study problems in the areas of geometric partial differential equations, mathematical physics, and dynamical systems. One will continue his investigation of geometric aspects of the Atiyah-Singer index theorem and the relationship between quantum field theory and low-dimensional topology. A second will continue an ongoing investigation of the harmonic map equation and its connections with Poisson-Lie structures and quantum groups. She will also investigate the Yang-Mills functional in dimensions larger than four. A third investigator will study the knot types of periodic orbits in the Lorenz attractor. Three investigators will continue ongoing projects involved in differential equations, topology, and mathematical physics. Differential equations relate the rate of change of one or more variables with respect to each other, or with respect to time. Topology is the mathematical study of shape. Both of these areas have a long history of use in mathematical physics.