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)
  • Sabin Cautis (representation theory, categorification, algebrai geometry)
Non-tenure-track faculty
Faculty from other groups with interests in geometry and topology
Graduate students
  • Russell Avdek (Honda)
  • Yin Tian (Honda)
  • Andrew Williams (Honda)
Recent graduate students, and thesis titles
  • Xiaobo Liu, Ph.D. 2005 (Bonahon), Representations of the quantum Teichmüller space.
  • David Crombecque, Ph.D. 2006 (Honda), Nonorientable contact structures on 3-manifolds.
  • Hua Bai, Ph.D. 2006 (Bonahon), Quantum hyperbolic geometry in dimensions 2 and 3.
  • François Guéritaud, Ph.D. 2006 (Bonahon), Hyperbolic geometry and canonical triangulations in dimension three.
  • Chris Hiatt, Ph.D. 2007 (Bonahon), Quantum traces in quantum Teichmüller theory
  • Roman Golovko, Ph.D. 2009 (Honda), The sutured embedded contact homology of solid tori
  • Sandra Ritz, Ph.D. 2009 (Honda), A categorification of the Burau representation via contact geometry
  • Julien Roger, Ph.D. 2010 (Bonahon), Factorization rules in quantum Teichmüller theory
  • Supap Kirtsaeng, Ph.D. 2010 (Honda), Embedded contact homology of a unit cotangent bundle via string topology
  • Guillaume Dreyer, Ph.D. (2012 (Bonahon),
  • Yang Huang, Ph.D. 2012 (Honda),