Scientific Program
The workshop consisted of whiteboard talks by participants on the following topics surveying Higher Teichmuller-Thurston Theory.
Speakers were be alotted 2-3 hours per talk. Speakers are also asked to submit a 5-6 page summary. For individual summaries, click on the talk titles, or download the full collection.
1. Brian Collier: Semi-simple Lie groups
Cartan decompositions, parabolic subgroups, associated symmetric spaces and their boundaries.
Suggested literature:
S. Helgason, "Differential Geometry, Lie Groups, and Symmetric Spaces" (selected chapters)
2. Spencer Dowdall: Anosov representations I
Definition and some properties.
Suggested literature:
O. Guichard, A. Wienhard "Anosov representations: Domains of discontinuity and applications" (first part)
3. Tengren Zhang: Anosov Representations II
Domains of discontinuity.
Suggested literature:
O. Guichard, A. Wienhard "Anosov representations: Domains of discontinuity and applications"
4. Andy Sanders: Hitchin representations
Construction with Higgs Bundles.
Suggested literature:
Selected by speaker.
5. Guilluaume Dreyer: Hitchin representations
Characterization of Hitchin representations.
Suggested literature:
F. Labourie "Anosov flows, surface groups and curves in projective space"
O. Guichard "Composantes de Hitchin et representations hyperconvexes de groupes de surface"
6. Tobias Hartnick: Maximal representations
Definition, properties of maximal and/or weakly maximal representations.
Suggested literature:
M. Burger, A. Iozzi, A. Wienhard "Surface group representations with maximal Toledo invariant"
M. Burger, F. Labourie A. Iozzi, and A. Wienhard "Maximal representations of surface groups: Symplectic Anosov structures"
7. Frederic Palesi: Positive representations
Mostly the case of SL(3, R), plus some comments on the case SL(n, R).
Suggested literature:
V. Fock, A. Goncharov "Moduli spaces of convex projective structures on surfaces"
V. Fock, A. Goncharov "Moduli spaces of local systems and higher Teichmuller theory" (some selected chapters)
8. Matthew Stover: Complex hyperbolic representations
Toledo invariant, rigidity results for lattices.
Suggested literature:
J. Marche, P. Will "Configurations of flags and representations of surface groups in complex hyperbolic geometry"
D. Toledo "Representations of surface groups in complex hyperbolic space"
W. Goldman, Millson "Local rigidity of discrete groups acting on complex hyperbolic space"
W. Goldman, M. Kapovich, B. Leeb "Complex hyperbolic manifolds homotopy equivalent to a Riemann surface"
M. Burger, A. Iozzi "Bounded Cohomology and Deformation Rigidity in Complex Hyperbolic Geometry"
9. Jeff Danciger: AdS representations
QuasiFuchsian AdS representations are Anosov.
Suggested literature:
T. Barbot "Quasi-Fuchsian AdS representations are Anosov"
Q. Merigot "Anosov AdS representations are quasi-Fuchsian"
10. Fanny Kassel: Convex cocompact representations
Discuss the fact that convex cocompact representations form the interior of deformation space and some equivalent definitions for Kleinian groups, followed by issues with generalizing to higher dimensions.
Suggested literature:
J-F. Quint, "Groupes convexes cocompacts en rang superieur"
B. Kleiner, B. Leeb "Rigidity of invariant convex sets in symmetric spaces"
11. Qiongling Li: SL(3, R)
Goldman-Choi paper and/or Labourie-Loftin paper.
Suggested literature:
W. Goldman "Convex real projective structures on compact surfaces"
S. Choi, W. Goldman "Convex Real Projective Structures on Closed Surfaces are Closed"
the following may also be useful:
S. Choi, W. Goldman "The classification of real projective structures on compact surfaces"
12. Sam Ballas: Sp(4, R)
Guichard-Weinhard construction of a domain of discontinuity.
Suggested literature:
O. Guichard, A. Wienhard "Convex foliated projective structures and the Hitchin component for PSL(4,R)"