Topology and Differential Geometry

Research in analytic topology continues in the broad area of generalized metric spaces. Also, current research is being carried out on topological groups and semi-groups, homogeneity properties of Euclidean sets, and finite-to-one mappings. There are weekly seminars on current research in analytic topology for both faculty and graduate students featuring non-departmental speakers.

This group studies relativity theory and differential geometry, with emphasis on twistor methods. One exciting recent project has been to show how some of the completely integrable systems from inverse scattering theory, such as the Korteweg-de Vries equation and the nonlinear Schrodinger equation, can be derived from the anti-self-dual Yang Mills equations.

The group also studies geometric and topological aspects of quantum field theory, string theory, and M-theory. This includes orientations with respect to generalized cohomology theories, and corresponding description via higher geometric, topological, and categorical notions of bundles.

DeBlois' Research (Assoc. Professor)

Jason DeBlois' research focus is in low-dimensional topology and hyperbolic geometry; broadly speaking, Dr. DeBlois studies the classification of three-manifolds from the perspective of the geometrization theorem. Some specific recent projects have studied hidden symmetries of hyperbolic knot complements, packings of hyperbolic surfaces, and low-volume hyperbolic three-manifolds. Dr. DeBlois has secondary interests in related fields such as geometric group theory, geometric analysis, and algebra.