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Higher Invariants Oberseminar (HIOB)

The Higher Invariants Oberseminar (HIOB) for the winter semester 2015 will study

  The Grothendieck-Teichmüller Group

Rather than survey the diverse appearances of the Grothendieck Teichmüller group within different subjects, we will concentrate on understanding two theorems:

I. There is an embedding Gal(Q/Q) —> GT of the absolute Galois group of the rational number field into the Grothendieck-Teichmüller group.

II. The Grothendieck-Teichmüller group is isomorphic to the group of homotopy automorphisms of the profinite completion of the little 2-discs operad.

We plan to spend roughly half of the semester on each of these theorems. There will be a brief interlude between parts I and II explaining the action of GT on the Teichmüller tower of moduli spaces of spheres with marked points, and the role of the braid groups.

Dates and location

Mondays, 14.00--16.00 in M102.


The seminar program is available here.


If you are interested in giving a talk in this seminar, please select a topic and enter your name in the schedule below:

  Date Title Speaker Notes
1. 12.10. Introduction and overview John Lind
2. 19.10 The étale fundamental group Johannes Sprang
3. 26.10 Curves and function fields Alexander Voitovitch
4. 02.11 Belyi's Theorem I Koen van Woerden
5. 09.11 Belyi's Theorem II Florent Martin
6. 16.11 Lifting the action of Gal(Q/Q) Johann Haas
7. 23.11 The monomorphism Gal(Q/Q) —> GT Niko Naumann
8. 30.11 Operads, discs, braids Tom Fiore Operads, Discs, Braids I
9. 07.12 [seminar cancelled]
10. 14.12 Profinite completion Oriol Raventós
10. 21.12 Operads, discs, braids II Dr. Thomas Fiore Operads, Discs, Braids II
12. 11.01 GT and the braid groups II Ulrich Bunke
13. 18.01 An overview of the proof Geoffroy Horel
14. 25.01 Weak operads Dmitri Pavlov
15. 01.02 GT = hAUT(E2) Kim Nguyen

Previous instance of HIOB