Séance Séminaire

Séminaire Gaston Darboux

Discrete Riemann Surfaces

I will give a survey of the theory of discrete Riemann surfaces, the linear and the quadratic ones (circle patterns), present the major theorems (harmonicity, Hodge theorem, quasi-conformal maps, existence of forms with given poles and holonomies, discrete polynomials and exponentials), show examples of discrete holomorphic functions and describe an algorithm to compute these functions.