Universität Wien

250158 VO Topics Course Mathematical Logic (2022W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
ON-SITE
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

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

Information

Aims, contents and method of the course

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.

Assessment and permitted materials

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

Minimum requirements and assessment criteria

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.

Examination topics

Reading list

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.

Association in the course directory

MLOV

Last modified: Fr 24.02.2023 11:49