Jun 05, 2019 from 04:15 PM to 05:45 PM

LMS 4 - Raum 325 - Seminarhörsaal

Abstract:

The aim of these lectures is to give a quick introduction to Grothendieck’s theory of dessins d’enfants. The main points I will attempt to explain are:

1. There is a bijective correspondence between compact Riemann surfaces and complex algebraic curves F (x, y) = 0.

2. The Riemann surfaces which correspond to polynomials F (x, y) whose coefficients are algebraic numbers are precisely those that admit a mero-morphic function with 3 branch points (Belyi’s theorem).

3. All these Belyi Riemann surfaces (i.e. all curves with algebraic coeffi-cients) can be represented by certain graphs embedded in a topological surface (dessins d’enfants).

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