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

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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.