Syllabus

• Week 1 (Note: this is a half week.)
  • Brief generalities on Lie groups and manifolds
  • The conformal group; the Poincare model of the hyperbolic plane
  
  
• Week 2
  • The projective and Lorenz group; other models of the hyp. plane
  • constructing hyperbolic surfaces and manifolds
  • topology of Teichmuller space; Fenchel-Nielson coordinates.
  
  
• Week 3 No class: ICERM geometric structures workshop
  
  
• Week 4
  • quasi-isometries and quasi-conformal maps
  • Mostow Rigidity
  
  
• Week 5
  • Cauchy rigidity for convex polyhedra
  • Cone surfaces and translation surfaces
  • The Veech group
  
  
• Week 6
  • Geometry of C2 and the Hopf fibration
  • Intro to complex hyperbolic space
  
  
• Week 7
  • Complex hyperbolic triangle groups: survey
  • My proof of the Goldman-Parker conjecture
  
  
• Week 8
  • The last ideal triangle group
  • Some account of my CR surgery theorem
  
  
• Week 9
  • Thurston's butterfly moves and real hyperbolic orbifolds.
  • Intro to Thurston's paper: shapes of polyhedra
  
  
• Week 10 shapes of polyhedra, cont.
  
  
• Week 11 shapes of polyhedra, cont.
  
  
• Week 12 Goldman's paper on convex projective structures
  
  
• Week 13 Margulis spacetimes
  
  
• Week 14
  • Nil geometry
  • Solv geometry
  • AdS geometry