Homotopy Theory and It's Applications

University Of Washington, Seattle WA

Investigators

Abstract

Mitchell's project has two principal components. The first is a study of K(1)-local homotopy theory and its applications, including applications to algebraic K-theory and general linear group homology. The methods incorporate an Iwasawa theory for K(1)-local spectra. The second component is an investigation of the topology and geometry of loop groups and symmetric spaces, including a homology Schubert calculus for the Pontrjagin ring and questions about stable homotopy type. Algebraic topology is the branch of geometry that studies qualitative properties of geometric objects, especially properties that remain invariant under continuous deformation. Topology has many connections to other branches of mathematics, and in recent years has appeared with surprising frequency in the sciences, including physics and even molecular biology. Mitchell's project is an investigation of intriguing new connections between algebraic topology, number theory, and the geometry of Lie groups (groups of transformations of manifolds and other geometric objects).