Higher Invariants Oberseminar: The Grothendieck-Teichmüller group

Content / Literature / Recommended previous knowledge The Higher Invariants Oberseminar (HIOB) for the upcoming semester 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) —> 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.

Prüfungsbestandteile Vortrag, schriftliche Ausarbeitung; je nach zutreffendem Modulkatalog ist entweder der Vortrag oder die schriftliche Ausarbeitung eine Studienleistung. Giving a presentation, writing a detailed report; depending on the applicable Modulkatalog: either the presentation or the written report is a Studienleistung.

Anteile der Bestandteile an der Note Je nach zutreffendem Modulkatalog basiert die Note entweder auf der schriftlichen Ausarbeitung oder auf dem Vortag. Depending on the applicable Modulkatalog: the grade is based either only on the written report or only on the presentation.