DATE |
PRESENTER
|
TOPIC
|
Sep
24 |
Alireza
|
Fundamental
concepts
Parallel postulate. Different models. Hyperbolic metric.
Möbius
transformations. Description of the geodesics in the hyper-half plane
model. |
Oct
1 |
John
Stogin |
Hyperbolic
area and trigonometry
Poincaré dics model, Gauss-Bonnet, The sine rule, The cosine
rule I, II.
PDF |
Oct
8 |
Alireza
|
Isometries
and geometry
Full group of isometries, Distance from a line, Perpendicular bisector,
Common orthogonal of
disjoint geodesics, hypercycle |
Oct
15 |
David
Sprunger |
Fuchsian
groups
Properly discontinuous actions. |
Oct
22 |
David
Sprunger
Juan Miguel Ogarrio |
Elementary
Fuchsian groups
Classification of isometries, Abelian Fuchsian groups, Classification
of elementary Fuchsian groups.
PDF |
Nov
5 |
Juan
Miguel Ogarrio |
Non-elementary
Fuchsian
groups
Discreteness criteria. |
Nov
12 |
Juan
Miguel Ogarrio |
Non-elementary
Fuchsian
groups
Jorgensen inequality. PDF
|
Nov
19 |
Marli
Wang |
Fundamental
domains
Modular group. PDF
|
Dec 3 |
Alireza |
Fundamental
domains
Drichlet domains, locally finite. |
Dec 10 |
Tim Campion |
Fundamental
domains
Ford fundamental domains, Quotient space. PDF
|
Dec 17 |
John Stogin
|
Geometrically finite
Possible covolumes of Fuchsian groups. PDF
|
Jan 10 |
Marli Wang
|
Uniformization
theorem
Hyperbolic surface, Hopf-Rinow theorem, Uniformization theorem. PDF |