Presentation topics

• The Pseudosphere and curvature of surfaces of revolution
• Limit sets of discrete groups
• Infinite type surfaces
• Modular curve
• Moduli space and/or Teichmuller space of hyperbolic surfaces
• Geodesic flow (see Einsiedler-Ward "Ergodic Theory with a view towards Number Theory.")
• Horocycle flow (see Einsiedler-Ward "Ergodic Theory with a view towards Number Theory.")
• Geodesic laminations
• Shear coordinates
• Properties of the mapping class group
• Bieberbach Theorem
• Delta hyperbolic spaces
• Hyperbolic geometry in complex dynamics (see Milnor "Complex Dynamics")
• Mostow rigidity
• Prime decomposition of 3-manifolds
• Hyperbolic structure on figure 8 knot complement
• Nil geometry
• Sol geometry
• Siefert fiber spaces
• Foliation as a geometric structure