Map enumeration problem

Dessin d’enfant (child’s drawing, map) is a graph embedded into a two-dimensional surface. The term was introduced by A. Grothendieck in 1984 in his famous "Esquisse d’un Programme". The theory of dessins d’enfants in a beautiful way connects 19th century complex analysis with 20th century arithmetic geometry, and very simple and intuitive objects with very abstract concepts. Besides brief overview of the topic the talk will present some results in one specific area, which is enumeration of graphs of certain type.