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Jan Draisma Professor of Mathematics Contact Publications Programs Talks Teaching Service Recreational
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TeachingInvariant Theory with ApplicationsThis course is taught in Fall 2009, by Dion Gijswijt and myself. Moreover, Bart Frenk is in charge of the exercise classes. See also the course page at Mastermath. There you also find where the course is (this varies heavily from week to week, due to an unfortunate planning error). As of 22 September, the course starts at 14:10 rather than 14:00, so that students following courses in Utrecht until 13:00 can make it.NOTE: THE LECTURE AND EXERCISE CLASS ON 10 NOVEMBER HAVE BEEN CANCELLED! THE NEXT LECTURE IS ON 17 NOVEMBER. Course materialSummaries of the material covered on Tuesday in week x will appear here around week x. These summaries contain some exercises that you can work on during the exercises sessions. Moreover, we require that you solve and hand in the extra homework problems below by the next lecture. Your final grade for this course will depend (only) on your results on these homework problems.Week 1 (8 September); with homework to be handed in by 15 September. Weeks 1 and 2 (15 September); homework, to be handed in by 22 September, consists of exercises 2.3.1 and 2.3.2. Week 1,2,3 (22 September); with homework to be handed in by 29 September. Week 1--4 (29 September); with homework to be handed in by 6 October. Week 1--5 (6 October); with homework to be handed in by 20(!) October; with some extra hints. Week 1--6 (13 October); homework to be handed in by 20(!) October: 6.1.6 and 6.3.6 Week 1--7 (20 October); homework to be handed in by 27 October: 7.0.16 and 7.0.17. Note: Chapter 6 was also expanded a little. Hint for 7.0.17: what are the orbits of G on W? Complete the square! Week 1--8 (27 October); with homework to be handed in by 3 November. Week 1--9 (3 November); homework to be handed in by 17(!) November: exercises 9.2.4 and 9.2.5. NOTE: THE LECTURE AND EXERCISE CLASS ON 10 NOVEMBER HAVE BEEN CANCELLED! THE NEXT LECTURE IS ON 17 NOVEMBER Week 1--10 (17 November); with homework to be handed in by 24 November. Week 1--11 (24 November); homework to be handed in by 1 December: 11.2.3 and 11.3.6. Week 1--12 (1 December); homework to be handed in by 8 December: 12.4.6. Late homework can be handed in until 18 December, by e-mail to Dion and Jan! (NOT to Bart!) Further readingTexts for collateral reading (in author-alphabetical order):Harm Derksen and Gregor Kemper, Computational invariant theory. (Takes a more algorithmic approach than most of the books below.) Roe Goodman and Nolan R. Wallach, Symmetry, representations, and invariants. (Based in part on the book originally published by Cambridge University Press, 1998. A very comprehensive textbook; also available online for those (institutions) with a subscription. Hanspeter Kraft and Claudio Procesi, Classical Invariant Theory, a Primer. (A concise introduction.) Mara Neusel, Invariant Theory. (More introductory than the other books. Recommended if you don't feel completely comfortable with notions such as group, ring, algebra.) Claudio Procesi, Lie groups. An approach through invariants and representations. (A very extensive textbook.) Bernd Sturmfels, Algorithms in invariant theory. (Takes a more algorithmic approach, like the book of Derksen and Kemper.) |