Mathematical Sciences: Differential Equations and Algebraic Groups and Their Representations - Discrete Subgroups of Semisimple Lie Groups

这个项目是关于李群及其表示的数学研究。这样的群，例如球体的旋转群，是很重要的，因为它们体现了数学许多领域中出现的情况的对称性。目前的工作预计将与微分几何和代数几何、数论、微分方程和代数群理论有高度的联系。更具体地说，Millson教授将研究从李群中的晶格到另一个李群的同态空间，并将研究与正交群和酉群相关的局部对称空间的几何问题。Varadarajan教授将研究亚纯微分方程，不变微分方程和振荡积分，以及约化群作用的不变分析。

This project is mathematical research on Lie groups and their representations. Such groups, for instance the group of rotations of a sphere, are important because they embody the symmetries of situations that arise in many areas of mathematics. The present work is expected to have a high degree of contact with differential and algebraic geometry, with number theory, with differential equations, and with the theory of algebraic groups. More specifically, Professor Millson will study spaces of homomorphisms from a lattice in a Lie group to another Lie group, and will also pursue geometric questions concerning locally symmetric spaces associated to orthogonal and unitary groups. Professor Varadarajan will work on meromorphic differential equations, invariant differential equations and oscillatory integrals, and invariant analysis for reductive group actions.