Permanent Faculty

  • James Cantrell Professor Emeritus. Geometry and topology.
  • Jason Cantarella Professor. General area of geometric knot theory, particularly random knots.
  • David Gay  Professor. Smooth and symplectic topology of 4-manifolds and associated 3-dimensional issues. Also interested in mathematical illustration and outreach, heavily motivated by low-dimensional geometry and topology.
  • John G. Hollingsworth Professor Emeritus. Geometry and Topology.
  • William H. Kazez  Professor. Contact topology and foliation in 4- and 3-manifolds, Heegaard Floer homology.
  • Gordana Matic  Professor. 4- and 3-manifolds, contact topology, Heegaard Floer homology.
  • Clinton G. McCrory Professor Emeritus. Topology of singularities, with applications to algebraic geometry and differential geometry. Invariants of real algebraic varieties and semialgebraic sets.
  • Trent Schirmer Lecturer. Low-dimensional geometric topology.  Visual and combinatorial methods to prove things about Heegaard splittings of 3-manifolds, Dehn fillings of link complements, and trisections of 4-manifolds.  The rank-genus problem for knot complements in the three-sphere, the slice-ribbon conjecture, and the Schoenflies conjecture.
  • Michael Usher Professor. Sympletic topology, Hamiltonian dynamics and Morse theory, symplectic four-manifolds and Lefschetz fibrations.
  • Weiwei Wu  Assistant Professor.  Topological rigidity of symplectic and Lagrangian submanifolds, symplectomorphism groups, Lagangian Floer theory, homological mirror symmetry. 


  • Jeffrey Meier Knot theory, knotted surfaces, and the topology of three-manifolds and four-manifolds. In particular, trisections of four-manifolds; four-dimensional knot theory,  surgery operations, and bridge trisections; various aspects of knot concordance, including doubly slice knots, fibered ribbon knots, and applications of knot homology theories; and Dehn surgery, especially exceptional surgery and Seifert fibered surgery.
  • Adam Saltz Connections between link homology theories, gauge theory, and symplectic topology with applications to contact and geometric topology. Also interested in the algebraic structure of these connections and how they can help us find new invariants.
  • Juanita Pinzon-Caicedo (adjunct assistant research scientist) The interplay between gauge-theoretic invariants and topological constructions; on the constructive side, most current efforts have been concentrated around the development of the theory of trisections for 4–manifolds with boundary and of embedded surfaces in B^4, on the gauge-theoretical side, mostly focused on the instanton moduli space.

Graduate Students