Topology and Geometry Research Group

Research Faculty

  • Daniel S. Freed ( Research interests include global analysis, differential geometry, relations with quantum field theory and string theory.
  • Robert E. Gompf ( Research interests include topology of 4-manifolds, gauge theory and its applications to topology, topology of algebraic surfaces, symplectic topology, and contact geometry.
  • Cameron McA. Gordon ( Research interests include manifold topology, with particular emphasis on knot theory and 3-dimensional manifolds. Dr. Gordon's future research plans are to continue working on problems in low-dimensional manifold topology, especially those related to classical knot theory.
  • Gary C. Hamrick ( Research interests include the relations between the geometry and the topology of manifolds.
  • Sean M. Keel ( Research interests include Algebraic Geometry, particularly Mori's program, GIT, moduli problems, and intersection theory.
  • John E. Luecke ( Research interests include the topology and geometry of 3-dimensional spaces. In particular the study of how the operation of "Dehn surgery" on a knot in 3-dimensional space affects the topology of the space. He has also spent time working with the application of topology to biology in understanding the knotting of DNA.
  • Alan W. Reid ( Research interests include low-dimensional topology and discrete groups. He is particularly interested in the geometry and topology of hyperbolic 3-manifolds, and properties of their fundamental groups. He is also interested in connections between hyperbolic 3-manifolds and number theory..
  • Lorenzo Sadun ( Research interests include quantum mechanics, nonperiodic tilings, adiabatic limits of wave equations, and other problems of bith physical and geometric interest.
  • Michael P. Starbird ( Research interests include low dimensional geometric topology and topics in mathematics education - particularly how to make mathematics accessible to the general public.
  • Karen K. Uhlenbeck ( Research interests include Global analysis and differential geometry with a special interest in applications of non-linear analysis in topology; solutions of Yang-Mills and Sine-Gordon equations; the topology of moduli spaces.
  • James W. Vick ( Research interests include topics from algebraic and differential topology involving actions of groups on manifolds, bilinear forms and Witt groups. A secondary research interest is in mathematical models and applications of mathematics to problems in the life sciences.
  • Robert F. Williams ( Research generally relates to Dynamical Systems. Currently, symbolic dynamics and matrices with entries in the positive integers. In particular, a partial converse to the Perron-Frobenius theorem. This takes one into "higher dimensional continued fractions".