University of Connecticut

Geometry and Topology

Research Activity

  • In differential geometry the current research involves submanifolds, symplectic and conformal geometry, as well as affine, pseudo-Riemannian, Riemannian and complex geometry and Riemannian geometry of infinite-dimensional manifolds.
  • In the area of geometric topology the emphasis is on low dimensional manifold theory, Kleinian groups and related decision problems. Areas of special interest include braid theory,¬†3-manifolds¬†and hyperbolic orbifolds, normal surface theory, group actions on manifolds, and applications of computational topology to computer animation, scientific visualization and engineering design.
  • In algebraic geometry: global and local positivity properties of numerical cycle classes and of vector bundles, asymptotic invariants.
  • In geometric analysis: heat kernel analysis on Lie groups and Riemannian manifolds, metric diophantine properties of the geodesic flow on a hyperbolic Riemann surface,¬†mathematical general relativity and geometric evolution equations.