discipline

Mathematics

subject

Riemann surfaces

lecturers

Gábor Halász

credits

2

period

second semester

curriculum

Abstract definition.

 

Covering. Continuation along curves, homotopy, Monodromy theorem, universal covering, covering group.

 

Dirichlet problem, Perron method. Green function. Homology. Residue theorem.

 

Classification of simply connected surfaces, their Riemann mapping theorems.

 

Recovering the surface from the covering group. Hyperbolic geometry. Discontinuous groups of linear fractional transformations. Fundamental region, fundamental polygon.

 

Riemann surface of analytic functions. Compact surfaces and complex algebraic curves.

 

literature

 

form of tuition

Lectures

mode of assessment

oral exam