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Hinweis Bitte informieren Sie sich auf den jeweiligen GRIPS-Seiten über den digitalen Ablauf der Lehrveranstaltungen.  Note For our digital courses all relevant information can be found on the appropriate GRIPS sites.Galois Groups and Fundamental Groups SemesterSoSe 2021 Lecturer Sebastian Wolf Type of course (Veranstaltungsart) Seminar Contents There are many formal analogies between the classical Galois theory of fields and the theory of covering spaces in algebraic topology. In this seminar we will see that, in certain situations over the complex numbers, this intuition can be turned into a theorem, using Riemann surfaces as a bridge between the two worlds. As an application of this theory, we will compute the absolute Galois group of the complex function field C(t). We will roughly follow the first three chapters of Szamuely's book "Galois Groups and Fundamental Groups". No previous knowledge of covering spaces or Riemann surfaces will be required, as we will introduce these notions during the seminar. If you are already familiar with these, it will still be interesting for you to see how these notions interact from a Galois-theoretic viewpoint. Literature Tamás Szamuely: Galois Groups and Fundamental Groups Recommended previous knowledge Algebra, Commutative Algebra, Complex Analysis Time/Date tba Location Digital Course homepage https://homepages.uni-regensburg.de/~wos07573/SeminarGalois.html (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
We might switch to meeting in person if it becomes possible during the semester. Modules BSem, MV, MSem ECTS Siehe Modulkatalog. MV und Nebenfach: 4,5 LP bei Studienbeginn ab WS 15/16, 6 LP bei Studienbeginn vor WS 15/16 |