Instructor:
Moon
Duchin
Office: Kerr 673, 48158
Office Hours: by appointment (mduchin@math)
Course meets: Wellman 125, Tuesdays and Thursdays, 4:406pm
....[no class Thursday
November 3]
Announcements and
Handouts and
Whatnot
Text  Svetlana Katok, Fuchsian Groups, Chicago Lectures in Mathematics 


Background  Katok writes that the book is intended for a onequarter graduate course, assuming only "a basic knowledge of real and complex analysis and abstract algebra." In fact, I think this overstates the prerequisites for reading most of the book for at least the first several chapters, what is required is calculus, comfort manipulating complex numbers, group theory, and familiarity with matrices. Despite its humble starting point, the text is a great segue into quite sophisticated mathematics.  
Outline  Text I. Hyperbolic Geometry II. Fuchsian Groups III. Fundamental Regions IV. Geometry of Fuchsian Groups V. Arithmetic Fuchsian Groups 
Supplementary Topics History of nonEuclidean geometry; axiomatics Flat surfaces Curvature and the GaussBonnet Theorem Flat structures on hyperbolic surfaces Lattices Threemanifolds and Kleinian groups; Geometrization 
Expectations  At the beginning, there will be a small number of required problems to make sure that everyone can work with the basic objects comfortably. After we have covered the core material of chapters 13, the emphasis will shift to projects. The last several course meetings will be devoted to presentations. 
Links
Supplementary Sources