Seminar on generalised formal power series and related topics

Organisers: Michele Serra, Prof. Dr. Salma Kuhlmann
Time: Wednesdays 15:15 - 16:45
Place: D 432
First talk: Wednesday, 13 April 2022 (preliminary date)
Target group: from 4th semester on
Prerequisites: Linear Algebra I and II and Algebra I and II.
Languages: English / German

Here you can find an overview sheet and some slides presenting the general mathematical context.


Goal
The aim of this seminar is to introduce generalised formal power series and to study their properties and their connections with several other branches of Algebra and Maths in general.

Procedure
Before their talk, each participant will send a title and an abstract to the seminar supervisor at latest 24 hours before the talk takes place.
A handout (max. 10 pages) must be available to all the participants by the time the talk starts: either send a copy to the supervisor
no later than 24 hours before the talk or, if the talk takes place in presence, bring along enough printed copies for all attendants.
The handout should be selfstanding and not just consist of the notes you use to give your presentation. It should allow the reader to fully understand the content of your talk and contain any details that the presentation time does not allow to cover.

Schedule

  • 13.04.2022: Michele - Introduction 1: Definition und erste Eigenschaften von verallgemeinerte Potenzreihenkörper

  • 20.04.2022: Michele - Introduction 2: Neumanns Lemma

  • 27.04.2022: Michele - Introduction 3: Bewertungen auf verallgemeinerten Potenzreihenkörper

  • 18.05.2022: Michele - Introduction 4: Automorphismen verallgemeinerter Potenzreihenkörper

  • 25.05.2022: Melissa - Graphenfärbung und die chromatische Zahl der Ebene

  • 01.06.2022: Salisha - Bewertete Vektorräume: Skelett und Bewertungsbasen

  • 29.06.2022: Lasse - Nichtarchimedische reel abgeschlossene Körper anhand von Potenzreihen

  • 06.07.2022: Alina - Hensel's Lemma auf den ganzen p-adischen Zahlen

  • 13.07.2022: David - Group rings

General literature

  1. S. Kuhlmann, Ordered Exponential Fields, Fields Inst. Monogr. 12 (Amer. Math. Soc., Providence, RI, 2000).

  2. S. Kuhlmann, Skript zur Vorlesung Reelle Algebraische Geometrie II, SS 2019

  3. A. J. Engler and A. Prestel, Valued Fields, Springer Monogr. Math. (Springer, Berlin, 2005).

  4. S. Prieß-Crampe, Angeordnete Strukturen: Gruppen, Körper, projektive Ebenen, Ergeb. Math. Grenzgeb. (2) 98 (Springer, Berlin, 1983).

  5. Literature on specific topics will be provided in due course