Universität Wien

250158 VO Topics Course Mathematical Logic (2022W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
VOR-ORT
Moodle

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Details

Sprache: Englisch

Prüfungstermine

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

  • Dienstag 04.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 06.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 11.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 13.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 18.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 20.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 25.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 27.10. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 03.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 08.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 10.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 15.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 17.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 22.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 24.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 29.11. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 01.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 06.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 13.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 15.12. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 10.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 12.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 17.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 19.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 24.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Donnerstag 26.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01
  • Dienstag 31.01. 13:15 - 14:45 Seminarraum 10, Kolingasse 14-16, OG01

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

This class will be an introduction to algebraic and model-theoretic aspects of differential fields, with a particular emphasis on the Galois theory of linear differential equations. This theory, which goes back to Picard and Vessiot at the end of the 19th century, parallels the Galois theory of algebraic equations. The differential Galois group carries the structure of a linear algebraic group, hence Picard-Vessiot theory served as an important motivation for developing the theory of algebraic groups. The foundations of differential algebra were laid by Ritt in the early 20th century and much clarified and extended by Kolchin, who also put Picard-Vessiot theory on a firm basis. The rise of differential algebra went hand in hand with the early development of model theory. Phenomena arising in the former often served as an inspiration for the latter. This culminated in the applications of the model theory of differential fields in diophantine geometry in the 1990s by Hrushovski, Pillay-Ziegler, and others.

Art der Leistungskontrolle und erlaubte Hilfsmittel

Based on a few homework sets assigned over the course of the semester.

Mindestanforderungen und Beurteilungsmaßstab

I will try to make the course accessible for those with a basic knowledge of graduate algebra (groups, rings, fields) and a modicum of model theory on the level of our Master's course Introduction to Mathematical Logic. In particular, I will not assume that you attended my classes Model Theory I, II from last year. If in doubt about your preparation, ask me.

Prüfungsstoff

Literatur

I will follow my own notes, but some useful references for this class are:

I. Kaplansky, An Introduction to Differential Algebra, 2nd ed., Actualités Scientifiques et Industrielles, no. 1251, Publications de l'Institut de Mathématique de l'Université de Nancago, no. V, Hermann, Paris, 1976.

A. R. Magid, Lectures on Differential Galois Theory, University Lecture Series, vol. 7, American Mathematical Society, Providence, RI, 1994.

D. Marker, M. Messmer, A. Pillay, Model Theory of Fields, 2nd ed., Lecture Notes in Logic, vol. 5, Association for Symbolic Logic, La Jolla, CA; A K Peters, Ltd., Wellesley, MA, 2006.

M. van der Put, M. F. Singer, Galois Theory of Linear Differential Equations, Grundlehren der Mathematischen Wissenschaften, vol. 328, Springer-Verlag, Berlin, 2003.

Zuordnung im Vorlesungsverzeichnis

MLOV

Letzte Änderung: Fr 24.02.2023 11:49