Differential Galois Theory, Spring Term 2014
Schedule: On Tuesdays 12:00 - 13:20, room 311 at the Faculty of Mathematics of HSE (Vavilova 7)
Instructor: Florian Heiderich
Office hours: Tuesday, 3:30 pm - 5:00 pm, room 309
Topics planned to be discussed: differential rings, linear differential equations, differential modules, Picard-Vessiot theory, Hopf algebras, affine group schemes, theory of Tannaka categories, Tannakian approach to linear differential equations
Prerequisites: Algebra and basic algebraic geometry.
Literature:
Picard-Vessiot theory:- Teresa Crespo and Zbigniew Hajto. Algebraic groups and differential Galois theory, volume 122 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 2011.
- Andy R. Magid. Lectures on differential Galois theory, volume 7 of University Lecture Series. American Mathematical Society, Providence, RI, 1994.
- Marius van der Put and Michael F. Singer. Galois Theory of Linear Differential Equations. Springer, Berlin, 2003. Available online from the homepage of Michael Singer
- Moss E. Sweedler. Hopf algebras. Mathematics Lecture Note Series. W. A. Benjamin, Inc., New York, 1969
- Pierre Deligne. Catégories tannakiennes. In The Grothendieck Festschrift, Vol. II, volume 87 of Progr. Math., pages 111–195. Birkhäuser Boston, Boston, MA, 1990
- Pierre Deligne and James S. Milne. Tannakian categories. In Hodge cycles, motives, and Shimura varieties, Lecture Notes in Mathematics, Vol. 900, pages 101–228. Springer, 1982. A TeXed version is available from the homepage of James Milne.
- Saunders MacLane. Categories for the working mathematician, Graduate Texts in Mathematics, Vol. 5, Springer-Verlag, New York, 1971.