Jones, Gareth; Matematični kolokvij april 2008

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Dessins d'enfants

Gareth Jones

University of Southampton, Velika Britanija

10. april 2008

This talk is an elementary introduction to Grothendieck's theory of dessins d'enfants (children's drawings). It describes how the combinatorial theory of maps on surfaces (specifically embeddings of bipartite graphs in compact orientable surfaces) can be used to characterise those Riemann surfaces which are defined as algebraic curves over the field of algebraic numbers. In particular, we obtain a combinatorial insight into the Galois theory of algebraic number fields.

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