Galois, Grothendieck and Voevodsky

Abstract: The talk will start with discussing the common features of the three mathematicians from the title: their non-standard education and specific relations with the community, outstanding imagination, productivity and contribution to the mathematics of future. The main part will be devoted to the development of the Grothendieck ideas (mostly from "Esquisse d'un Programme") by Voevodsky, including the application of dessins d'enfants to the inverse Galois problem. Finally, some problems of univalent foundations will be mentioned in the context of dessins-labelled stratifications of moduli spaces of curves.