This is a website for the reading group on Dessins d'enfants on Riemann surfaces that we are doing in the Spring semester 2023/24 in Ljubljana.
The main reference is the book by Jones and Wolfart.
Each participant chooses a topic and prepares a 45 minute lecture for the group. You do not need to cover the whole material in great detail and it is completely OK to only explain the main ideas (after all, you only have 1 hour).
If you decide to participate, send an email to urban.jezernik@fmf.uni-lj.si so that I mark the topic has been chosen.
A list of topics together with references is available here (prepared by Micael Toledo).
General introduction to Riemann surfaces and related topics (Riccardo Ugolini)
Algebraic curves and their relation to compact Riemann surfaces. (Jon Mikoš)
Belyi functions and their dessins (Belyi's Theorem). (Izak Jenko)
A sketch of the proof of Belyi's Theorem. (Marko Čmrlec)
An introduction to maps, hypermaps, and their dessins. (Micael Toledo)
Main theorem of uniformisation theory (the extended Riemann mapping theorem). (Beno Učakar)
Triangle groups and Fuchsian groups. (Miloš Puđa)
Triangle groups and Belyi functions. An inclusion criterion for Fuchsian groups. (Andoni Zozaya)
Connection between dessins and holomorphic structures.
Introduction to Galois theory and the absolute Galois group. (Tim Milanez)
The action of the Galois group, finally! (Urban Jezernik)
We meet on Tuesdays at 14-15 in classroom 3.06.
12/03/2024 Micael Toledo: Introductory meeting
26/03/2024 Riccardo Ugolini: General introduction to Riemann surfaces and related topics [video]
02/04/2024 Jon Mikoš: Algebraic curves and their relation to compact Riemann surfaces
09/04/2024 Izak Jenko: Belyi functions and their dessins (Belyi's Theorem) [video (pass: DN7j7??T)]
16/04/2024 Marko Čmrlec: A sketch of the proof of Belyi's Theorem
23/04/2024 Micael Toledo: An introduction to maps, hypermaps, and their dessins [video]
30/04/2024 Miloš Puđa: Triangle groups and Fuchsian groups [video]
07/05/2024 Beno Učakar: Main theorem of uniformisation theory (the extended Riemann mapping theorem) [video]
14/05/2024 Andoni Zozaya: Triangle groups and Belyi functions. An inclusion criterion for Fuchsian groups [video]
21/05/2024 Urban Jezernik: Connection between dessins and holomorphic structures [video]
28/05/2024 Tim Milanez: Introduction to Galois theory and the absolute Galois group [video]
04/06/2024 Urban Jezernik: The action of the Galois group, finally! [video]