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)
  • Ko Honda (contact and symplectic geometry, Floer homology)
  • 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)
  • Michael Abrams (Lauda)
  • Bahar Acu (Honda)
  • Andrew Williams (Honda)
Recent graduate students, thesis titles, and placement
  • Xiaobo Liu, Ph.D. 2005 (Bonahon), Representations of the quantum Teichmüller space, Columbia University.
  • David Crombecque, Ph.D. 2006 (Honda), Nonorientable contact structures on 3-manifolds, Bryn Mawr College.
  • Hua Bai, Ph.D. 2006 (Bonahon), Quantum hyperbolic geometry in dimensions 2 and 3, University of Georgia.
  • François Guéritaud, Ph.D. 2006 (Bonahon), Hyperbolic geometry and canonical triangulations in dimension three, National Center for Scientific Research (CNRS), France.
  • Chris Hiatt, Ph.D. 2007 (Bonahon), Quantum traces in quantum Teichmüller theory, University of Texas of the Permian Basin.
  • Roman Golovko, Ph.D. 2009 (Honda), The sutured embedded contact homology of solid tori, Mathematical Sciences Research Institute.
  • Sandra Ritz, Ph.D. 2009 (Honda), A categorification of the Burau representation via contact geometry, USC.
  • Julien Roger, Ph.D. 2010 (Bonahon), Factorization rules in quantum Teichmüller theory, Rutgers University.
  • Supap Kirtsaeng, Ph.D. 2010 (Honda), Embedded contact homology of a unit cotangent bundle via string topology, Kasetsart University, Thailand.
  • Guillaume Dreyer, Ph.D. 2012 (Bonahon), Geometric properties of Anosov representations, University of Notre Dame.
  • Yang Huang, Ph.D. 2012 (Honda), On the homotopy of 2-plane fields and its applications in contact topology, Max Planck Institute, Germany.
  • Russell Avdek, PhD 2013 (Honda), Contact surgery, open books, and symplectic cobordisms, Zoosk Inc.
  • Yin Tian, Ph.D. 2014 (Honda), A categorification of sl(1|1) via contact topology, Simons Center for Geometry and Physics.