Topology and Geometry Research Group

Research Faculty

• Daniel S. Freed (dafr@math.utexas.edu): Research interests include global analysis, differential geometry, relations with quantum field theory and string theory.
• Robert E. Gompf (gompf@math.utexas.edu): 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 (gordon@math.utexas.edu): 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 (hamrick@math.utexas.edu): Research interests include the relations between the geometry and the topology of manifolds.
• Sean M. Keel (keel@math.utexas.edu): Research interests include Algebraic Geometry, particularly Mori's program, GIT, moduli problems, and intersection theory.
• John E. Luecke (luecke@math.utexas.edu): 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 (areid@math.utexas.edu): 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 (sadun@math.utexas.edu): Research interests include quantum mechanics, nonperiodic tilings, adiabatic limits of wave equations, and other problems of bith physical and geometric interest.
• Michael P. Starbird (starbird@math.utexas.edu): 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 (uhlen@math.utexas.edu): 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 (vsjwv@utxdp.dp.utexas.edu): 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 (bob@math.utexas.edu): 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".