The 3rd MSJ-SI

The Mathematical Society of Japan, Seasonal Institute

Development of Galois-Teichmüller Theory
and Anabelian Geometry

October 25 Monday, 10:00--11:00
P. Cartier (IHÉS)
Towards Grothendieck's "Dessins d'Enfants"
During his Montpellier period, Grothendieck changed his style and the focus of his mathematical research. Perhaps motivated by the need to give "elementary" lectures, he became interested in a kind of more explicit mathematics. Already in a Cartan/Grothendieck seminar of 1961, he got interest in the construction of the Teichmuller space, to be used in the construction of the moduli space of compact Riemann surfaces. The new central tool was the Belyi theorem creating a connection between algebraic curves, number fields and certain combinatorial dissections ("dessins d’enfants"). This enabled him to formulate a very fruitful program in the well-known paper "Sketch of a program". We shall mention some possible connections with Maass automorphic forms.