RESEARCH: Geometry & Topology Group


The geometry/topology group at USC currently has an emphasis on the topology and geometry of low-dimensional manifolds and on contact and symplectic geometry.  This includes Floer homology theories, hyperbolic geometry, mapping class groups of surfaces, quantum invariants and topological quantum field theories. Our research has connections with and is motivated in part by string theory and mathematical physics.

Tenured and tenure-track faculty
  • Francis Bonahon (hyperbolic geometry, quantum invariants, higher Teichmüller theory)
  • Aaron Lauda (categorification, representation theory, and low-dimensional topology)
Non-tenure-track faculty
Faculty from other groups with interests in geometry and topology
Graduate students (post qualifying)
  • Bahar Acu (Honda)
  • Laffite Lamberto-Egan (Lauda)
  • Giuseppe Martone (Bonahon)
  • Can Oguz (Lauda)
  • Bin Tian (Honda)
Recent graduate students, thesis titles, and placement
  • Michael Abrams, Ph.D. 2016 (Lauda), Symmetries of categorified quantum groups.
  • Andrew Williams, Ph.D. 2015 (Honda), On the Giroux correspondence, Flintridge Academy.
  • Yin Tian, Ph.D. 2014 (Honda), A categorification of sl(1|1) via contact topology, Simons Center for Geometry and Physics.
  • Russell Avdek, PhD 2013 (Honda), Contact surgery, open books, and symplectic cobordisms, Zoosk Inc.
  • Yang Huang, Ph.D. 2012 (Honda), On the homotopy of 2-plane fields and its applications in contact topology, Max Planck Institute, Germany.
  • Guillaume Dreyer, Ph.D. 2012 (Bonahon), Geometric properties of Anosov representations, University of Notre Dame.
  • Supap Kirtsaeng, Ph.D. 2010 (Honda), Embedded contact homology of a unit cotangent bundle via string topology, Kasetsart University, Thailand.
  • Julien Roger, Ph.D. 2010 (Bonahon), Factorization rules in quantum Teichmüller theory, Rutgers University.