guillaumedreyer

Guillaume Dreyer

Visiting Assistant Professor

University of Southern California, Los Angeles, CA, United-States

  • Ph.D. in Mathematics, 2012
    Thesis Advisor: Prof. Francis Bonahon.

 

Email:  gdreyer@nd.edu

Office:  108 Hayes-Healy Hall
Phone:  (574) 631-8706
Fax:  (574) 631-6579

 

For additional information see Guillaume Dreyer's Personal Page. TBA

Research Interests

 

My research lies in the area of low dimensional topology and geometry. It is concerned with the study of surface group homomorphisms into a Lie group. The approach combines various tools and techniques from hyperbolic geometry, Lie group theory, dynamical systems and algebraic geometry. I am mostly focused on understanding geometric properties of "special" homomorphisms, such as positive representations, maximal representations, and more generally, Anosov representations.

The framework of special representations has proved to be quite convenient, as it offers a flexible and global approach that applies to most interesting surface group representations, which usually fall within one of these three categories. Important examples of special representations are given by representations lying in the Hitchin component of the associated character variety of a given Lie group. These Hitchin representations are of particular interest, as they generalize to higher rank Lie groups the notion of Fuchsian representation. Hitchin components thus correspond to Teichmüller components for higher rank Lie groups, so that their systematic study is now commonly referred to as "higher Teichmüller theory".

Research-wise, I am interested in analyzing how some concepts and techniques from classic hyperbolic geometry extend to higher Teichmüller theory. This includes the investigation of geometric invariants and deformations for Hitchin and Anosov representations, parametrizations of Hitchin components, symplectic and Poisson geometry of character varieties, compactification methods for Hitchin components.

Selected Publications

  • G. Dreyer, The space of Anosov representations along a geodesic lamination, in preparation.
  • F. Bonahon, G. Dreyer, Hitchin representations and geodesic laminations, in preparation.
  • G. Dreyer, Thurston's cataclysms for Anosov representations, preprint (2013), available at arXiv:1301.6961.
  • F. Bonahon, G. Dreyer, Parametrizing Hitchin components, submitted, available at  arXiv:1209.3526.
  • G. Dreyer, Length functions of Hitchin representations, submitted, available at arXiv:1106.6310.

Please direct questions and comments to:  gdreyer@nd.edu