Constructive Methods in Number Theory
with focus on modular forms and rational coverings
March 2nd – 6th, 2015
Dessins d'enfants and their realization as Belyi maps of compact Riemann surfaces were originally discovered by Felix Klein. Their importance and relevance was finally understood by
Alexander Grothendieck who rediscovered and named them in his "Esquisse d'un programme" in 1984. The most important aspect of dessins is the operation of the absolute Galois group on
them. Accordingly, dessins d'enfants provide fascinating insights and fundamental links between different fields of mathematics like inverse Galois theory, Teichmüller spaces, hypermaps,
algebraic number theory and mathematical physics. The related problem of the construction of Riemann surfaces with given automorphism group turns out to be rather challenging.
Recently there have been several attempts to attack this difficult problem with some success. However we are still far from understanding what Grothendieck called the tower of Teichmüller
groupoids. The goal of the workshop is to bring together experts from different fields of mathematics to share their insights and enlighten the connections between the algebraic,
geometric and number theoretic aspects of the problem.