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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 [http://homepages.uni-regensburg.de/~lij60053/papers/HIOB_GT.pdf 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:

<table>
<tr>
<td> </td>
<td>Date</td>
<td>Title</td>
<td>Speaker</td>
<td>Notes</td>
</tr>

<tr>
<td>1.</td>
<td>12.10.</td>
<td>Introduction and overview</td>
<td>John Lind</td>
<td></td>
</tr>

<tr>
<td>2.</td>
<td>19.10</td>
<td>The étale fundamental group</td>
<td>Johannes Sprang </td>
<td></td>
</tr>

<tr>
<td>3.</td>
<td>26.10</td>
<td>Curves and function fields</td>
<td>Alexander Voitovitch </td>
<td></td>
</tr>

<tr>
<td>4.</td>
<td>02.11</td>
<td>Belyi's Theorem I</td>
<td> Koen van Woerden</td>
<td></td>
</tr>

<tr>
<td>5.</td>
<td>09.11</td>
<td>Belyi's Theorem II</td>
<td>Florent Martin </td>
<td></td>
</tr>

<tr>
<td>6.</td>
<td>16.11</td>
<td>Lifting the action of Gal(Q/Q)</td>
<td>Johann Haas </td>
<td></td>
</tr>

<tr>
<td>7.</td>
<td>23.11</td>
<td>The monomorphism Gal(Q/Q) —> GT</td>
<td>Niko Naumann </td>
<td></td>
</tr>

<tr>
<td>8.</td>
<td>30.11</td>
<td>Operads, discs, braids</td>
<td>Tom Fiore </td>
<td>[http://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/fioreoperadsdiscsbraids1.pdf Operads, Discs, Braids I]</td>
</tr>

<tr>
<td>9.</td>
<td>07.12</td>
<td>[seminar cancelled]</td>
<td> </td>
<td></td>
</tr>

<tr>
<td>10.</td>
<td>14.12</td>
<td>Profinite completion</td>
<td>Oriol Raventós </td>
<td></td>
</tr>

<tr>
<td>10.</td>
<td>21.12</td>
<td>Operads, discs, braids II</td>
<td>Dr. Thomas Fiore</td>
<td>[http://www-app.uni-regensburg.de/Fakultaeten/MAT/sfb-higher-invariants/images/fioreoperadsdiscsbraids2.pdf Operads, Discs, Braids II]</td>
</tr>

<tr>
<td>12.</td>
<td>11.01</td>
<td>GT and the braid groups II</td>
<td> Ulrich Bunke </td>
<td></td>
</tr>

<tr>
<td>13.</td>
<td>18.01</td>
<td> An overview of the proof </td>
<td> Geoffroy Horel </td>
<td></td>
</tr>
<tr>
<td>14.</td>
<td>25.01</td>
<td>Weak operads</td>
<td>Dmitri Pavlov </td>
<td></td>
</tr>

<tr>
<td>15.</td>
<td>01.02</td>
<td>GT = hAUT(E2)</td>
<td> Kim Nguyen </td>
<td></td>
</tr>

</table>

== Previous instance of HIOB ==

* [[Higher_Invariants_Oberseminar| HIOB SS 2015]]

Higher Invariants Oberseminar WS1516 - Revision history

132.199.243.28: Created page with "__NOTOC__ =Higher Invariants Oberseminar (HIOB)= The Higher Invariants Oberseminar (HIOB) for the winter semester 2015 will study The Grothendieck-Teichmüller Group<..."

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