Deformations of Belyi maps and dessins d’enfant

Date: 18/11/2019
Time: 13:30 - 14:30


Belyi maps and their geometric representations - dessins d'enfant ("child drawings") - have appealing significance in algebraic geometry, number theory, combinatorics, transformations of modular and hypergeometric functions. Belyi maps are algebraic coverings of the Riemann sphere that branch only above 0, 1 or infinity. More generally, almost Belyi maps are algebraic coverings to ${\mathbb P}^1 \setminus \{0,1,\infty\}$ with exactly one additional (simple) branching point. They form 1-dimensional families, characterize algebraic solutions of the Painleve VI equations and corresponding isomonodromic Fuchsian differential equations. I describe the monodromy variation of almost Belyi maps and the corresponding geometric analogue of dessins d'enfants.