Quantized Geometry comprises three closely interconnected areas: (1) The Zeta functions of elliptic operators, which in topology and geometry are used to describe non-local numerical invariants like torsion, and in physics are related to functional integrals. (2) The geometry of certain infinite dimensional spaces and groups, which have appeared in algebraic topology in connection with the algebraic K-theory of topological spaces, in geometric topology in connection with the groups of automorphisms of manifolds, and in physics as mathematical models capable of incorporating new types of symmetry, like supersymmetry. (3) Operator algebraic methods which, with the advent of K- theory, became relevant to differential and topological geometry. This grant will enable a number of junior mathematicians to participate in a conference devoted to Quantized Geometry at the Ohio State University in May, 1991.
