Areas of Research in Geometry & Topology

Professors   Bruner , Drucker, Handel , Hu, Isaksen, Klein , Rhee,  and Schochet 

Algebraic topology is a discipline which uses the tools of modern algebra to attack geometric problems. Projects include questions about vector fields, immersions, and embeddings for smooth manifolds; the existence or non-existence of metrics of positive scalar curvature; the pursuit of connections between algebraic topology and parts of analysis (specifically operator algebras, approximation theory and measure theory on manifolds); group actions on manifolds; group cohomology and extraordinary cohomology theories of classifying spaces of groups; the classification of algebraic structures which arise in the study of H-spaces (a generalization of topological groups); multiplicative structures in homotopy theory; computer calculation of algebraic structures used in topology; localization and periodicity.

Areas of investigation in Differential Geomety include the geometry of and classification of special classes of curves and hypersurfaces in Euclidean space, the differential geometry of homogeneous spaces and its connection with non-associative algebra, and Lie theory.

Point set topology is a discipline which studies the topological structure of sets and mappings between sets. Projects include set valued maps; metric spaces; dimension theory.