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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.

Program

The seminar program is available here.

Talks

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

• HIOB SS 2015