Sergei Yakovenko's blog: on Math and Teaching

Tuesday, February 26, 2008

Semester II: tentative programme

Filed under: Analytic ODE course — Sergei Yakovenko @ 9:03
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The course on Analytic and Geometric Theory of Differential Equations resumes on Wed Feb 27, 2008.

Note the change in the schedule: in the second semester classes will be in Room 261, on Wednesdays (instead of Thursdays), still between 9:00 and 10:50 (apologies before those who suffer from the pre-dawn wake-up). Thursdays, from 14:00 till 16:00.

The second semester will be centered on the theory of linear systems, as exposed in Chapter III of the book (warning: the draft posted on my web page is really outdated. I will provide links to individual sections of the printed edition, with printing option disabled, as before, to protect the copyright).

More precise (albeit still provisional) plan is as follows.

  1. General properties of systems of linear ordinary differential equations in the complex domain. Gauge equivalence. Monodromy and holonomy.
  2. Local theory of singular points. Fuchsian, regular and irregular singularities.
  3. Towards the global theory of  linear systems: holomorphic vector bundles.
  4. Towards the global theory of linear systems: meromorphic connexions on vector bundles.
  5. Reconstruction of a linear system from its monodromy group. The Riemann–Hilbert problem.
  6. Positive results on solvability of the Riemann–Hilbert problem. Bolibruch–Kostov theorem.
  7. Negative results and the Bolibruch counterexample.
  8. Scalar high order linear ordinary differential equations and associated geometric structures. Hypergeometric equations.
  9. Irregular singularities: formal theory.
  10. Irregular singularities: elements of analytic theory. Stokes phenomenon.
  11. Elements of multidimensional theory: meromorphic flat connexions on \mathbb C^n.

The second semester is intended to be as independent from the first semester, as possible, so that newcomers may join at this junction.

Sunday, November 11, 2007

Disclaimer

Filed under: Analytic ODE course — Sergei Yakovenko @ 9:20
Tags: ,

Given the continuing strike of the senior academic staff and temporary suspension of lectures, classes and all other forms of the frontal eductation, this weblog changes itself into a Web-based Research Project for Masters Students at the Faculty of Mathematics and Computer Science, Weizmann Institute of Science.

Participation in the project is advised to first and second year students, yet Ph. D. students are also encouraged to attend.

Participants in the project are assumed to read weekly portions of research texts (monographs and articlkes)  regularly published on these pages.

There is a weekly meeting between the participants and the head of the project (S.Y.) every Thursday between 9:00 and 11:00. During this meeting the participants receive explanations and extended comments on especially difficult instances of the text and answers to their questions. Meetings are open to everybody.

For disambiguation purposes it should be understood that:

  1. This research project is in no way related to the course “Analytic and Geometric Theory of Ordinary Differential Equations”, announced earlier. The regular course will start with the end of the strike.
  2. The students will not receive credit points for participation in the project: its purpose is to familiarize the prospective students with an ongoing research.

Don’t hesitate to ask any questions if you feel confused by this disambiguation 😉

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