9625336 Lipsman Professors Lipsman and Rosenberg plan to continue their respective work in group representation theory, analysis on homogeneous spaces, and C*-algebraic index theory. Professor Lipsman will study the Fourier analysis of homogeneous spaces, its relation to invariant differential operators and various orbital constructs, and the notion of distributional Frobenius reciprocity. Professor Rosenberg will study manifolds of positive scalar curvature, index theory on manifold-like spaces, and K-theory and L-theory of operator algebras. Professors Lipsman and Rosenberg will jointly study Paley-Wiener Theorems and uncertainty principles on Lie groups. The emphasis of this project will be on the interplay between analysis (for example, study of the solutions of partial differential equations) and geometrical structure, broadly interpreted. The relationship between analysis and geometry is one of the most important themes in modern mathematics and physics. Professors Lipsman and Rosenberg will also jointly work to help convey this theme to undergraduates by enhancing the usual multivariable calculus course with computer projects emphasizing the underlying geometrical and physical principles. ***
