Topics Seminar: Dessins d'Enfants

Fall 2007: Fridays 10:30-12, room 101

Description

This is a "learning seminar", organized by graduate students, with talks focusing on Grothendieck's theory of dessins d'enfants throughout the semester. All graduate
students and faculty are welcome to attend. The hope is that all interested participants will give at least one talk. Contact here

The theory of dessins d'enfants ("children's drawings") was part of plan started by A. Grothendieck in the mid-1980's to study the interplay between Galois theory
over Q and Riemann surfaces via simple and concrete combinatorial objects.

Our goal this term is to start from the beginning and prove as many theorems and understand as many examples as we can, with attention paid to the interplay between
algebraic geometry, topology, and number theory.

Schedule

Date

Speaker

Topic
September 14 Keefe San Agustin Introduction, the theorems of Weil and Belyi and an example
September 21 Tathagata Sengupta Voevodsky's butterflies; Proof of Belyi's Theorem
September 28 Tathagata Sengupta faithful Galois actions on dessins I
October 5 Keefe San Agustin The Grothendieck Correspondence
October 12 Kiyoshi Igusa Puissant series and monoidal categories
October 19 Leila Schneps Grothendieck-Teichmuller Theory
October 26 Kiyoshi Igusa Braided monoidal categories and GT
November 2 Tathagata Sengupta The Lego-Teichmuller Theorem I
November 9 Keefe San Agustin The Lego-Teichmuller Theorem II
November 16 You?? TBA

Links to papers we are reading

  • Dessins d'enfants on the Riemann Sphere, L. Schneps
  • Braid Groups and Galois Theory, F. Jarvis Notes from a course at Oxford.
  • Drawing Curves Over Number Fields by G.B. Shabat and V.A. Voevodsky. Not available on-line.
  • Dessins from a geometric point of view, Jean-Marc Couveignes and Louis Granboulan
  • A note on the action of the absolute Galois group on dessins Ernesto Girondo Galois actions are faithful in genus g>1. A 2 page paper!
  • Galois actions on dessins, David Burggraf a recent PhD thesis
  • On the Lego-Teichmuller game, B. Bakalov1 and A. Kirillov
  • Chebycheff and Belyi polynomials, dessins d'enfants, Beauville surfaces and group theory, Ingrid Bauer, Fabrizio Catanese, and Fritz Grunewald
  • Galois invariants of dessins d'enfants, Jordan Ellenberg
  • Belyi-Extending Maps and the Galois Action on Dessins d'Enfants, Melanie Matchett Wood
  • Teichmuller spaces, triangle groups and Grothendieck dessins, William Harvey

    • Participants

  • Alex Charis, Kiyoshi Igusa, Florian Klossinger, Alexander Oster, Keefe San Agustin, Tathagata Sengupta, Martin Sigl

    Conference

  • The Grothendieck-Teichmuller Theory of Dessins d'enfants Sep 8, 2008 - Sep 12, 2008, ICMS, Edinburgh

    This page is maintained by Keefe San Agustin; it was shamelessly copied from Jason Starr's page, which in turn was shamelessly copied from Ravi Vakil's page, which in turn
    was shamelessly copied from Pasha Belorousski's page at the University of Michigan. For more sites with a similar pedigree, see Michael Thaddeus's list or Jim Bryan's list

    .
    Brandeis University Department of Mathematics