DATE 
PRESENTER

TOPIC

Sep
24 
Alireza

Fundamental
concepts
Parallel postulate. Different models. Hyperbolic metric.
Möbius
transformations. Description of the geodesics in the hyperhalf plane
model. 
Oct
1 
John
Stogin 
Hyperbolic
area and trigonometry
Poincaré dics model, GaussBonnet, 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 
Nonelementary
Fuchsian
groups
Discreteness criteria. 
Nov
12 
Juan
Miguel Ogarrio 
Nonelementary
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, HopfRinow theorem, Uniformization theorem. PDF 