Mathematical Sciences: Differential Equations, Group Representations, and Mathematical Physics

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Professors Varadarajan and Babbitt will work on a variety of projects. The first is a joint project involving the study of differential equations in a broad framework which relates them to algebraic groups and their representations. The questions to be studied have broad significance in such areas as differential modules over schemes, moduli of vector bundles, theory of algebraic groups, asymptotic analysis, and invariant differential operators and distributions. Other projects involve representation theory of the Poincare group, and scattering theory in the quantum Heisenberg model. The joint project focuses on the behavior of solutions to differential equations with singularities as a function of external parameters. The other projects fall under the heading of mathematical physics and involve mathematical aspects of quantum theory.