Sergei Yakovenko's blog: on Math and Teaching

Saturday, March 1, 2008

Lecture 2 (Sun, Mar 2, 2008)

Local theory of regular singular points of linear systems

This lecture, in an exceptional way, will take place on Sunday, 16:00-18:00, in the Room 261.

  1. Regular and irregular singularities: growth matters.
  2. Local gauge equivalence (holomorphic, meromorphic, formal). Meromorphic classification of regular singularities.
  3. Fuchsian singularities as a particular class of regular singularities (Sauvage lemma).
  4. Formal classification of Fuchsian singularities (Poincaré-Dulac theorem revisited). Resonances. Levelt upper triangular normal form.
  5. Coincidence of formal and holomorphic classification in the Fuchsian case.
  6. Integrability of the normal form.
  7. Towards global theory of Fuchsian systems on \mathbb C P^1: Monopoles as special classes of rational matrix functions.

Reading: Sections 16A-16E from the Book (printing disabled).

Reminder: Today (actually, on Friday) was the deadline for submission of the home exam 😦


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