Universität Wien

250130 VO Algebraic Theory of Differential Equations (2020S)

5.00 ECTS (3.00 SWS), SPL 25 - Mathematik

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 03.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.03. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 10.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.03. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 17.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.03. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 24.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.03. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 31.03. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 01.04. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 21.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.04. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 28.04. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.04. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 05.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.05. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 12.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 13.05. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 19.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 20.05. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 26.05. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.05. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Wednesday 03.06. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 09.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.06. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 16.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.06. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 23.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.06. 09:45 - 10:30 Hörsaal 2 Oskar-Morgenstern-Platz 1 Erdgeschoß
  • Tuesday 30.06. 13:15 - 14:45 Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

In this course we will look at linear ordinary differential equations with polynomial, holomorphic or meromorphic coefficients from an algebraic point of view. As such, a rich panorama of techniques and results unfolds:

The Euler-Gauss hypergeometric differential equation, hypergeometric series, regular and irregular singular points, normal forms of ode's, Picard-Fuchs equations, Apéry's differential equation, irrationality of odd values of the zeta-function, modular forms and elliptic curves, the monodromy representation, the Riemann-Hilbert correspondence, differential Galois theory, fundamental groupds and analytic continuation, indicial equations, D-modules and the Weyl algebra, linear recursions, lattice walks, enumerative combinatorics.

Nevertheless, the approach will be mostly elementary and does not require a huge amount of prerequisites.

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

Reading list

Association in the course directory

MALV; MANV

Last modified: Mo 12.10.2020 13:29