Permanent Faculty

  • James Cantrell Professor Emeritus. Geometry and topology.
  • Jason Cantarella Professor. General area of geometric knot theory, particularly random knots.
  • David Gay  Associate 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 Associate 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, I have a great interest in 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.
  • Huygens Ravelomanana: 3-manifolds topology, knot theory and smooth 4-manifolds. In particular, I am interested in problem related to Dehn surgeries, homology theories for 3-manifolds and links or knots and 3-manifolds character varieties. For the moment I am focused on cosmetic  Dehn surgeries on arbitrary rational homology spheres and their relation to character variety.
  • Adam Saltz. the connections between link homology theories, gauge theory, and symplectic topology with applications to contact and geometric topology.  I'm also interested in the algebraic structure of these connections and how they can help us find new invariants.


Graduate Students