Universität Wien
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250096 VO Analysis on manifolds (2021S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 01.03. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 03.03. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 08.03. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 10.03. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 15.03. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 17.03. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 22.03. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 24.03. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 12.04. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 14.04. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 19.04. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 21.04. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 26.04. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 28.04. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 03.05. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 05.05. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 10.05. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 12.05. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 17.05. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 19.05. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 26.05. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 31.05. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 02.06. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 07.06. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.06. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 14.06. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.06. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 21.06. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.06. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock
  • Monday 28.06. 09:45 - 11:15 Digital
    Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.06. 09:45 - 11:15 Digital
    Seminarraum 7 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

This course is in the core modules for the area "geometry and topology" of the master program and provides the basis for large parts of this area. It discusses the basic theory of (abstract) smooth manifolds and analysis thereon, which is the foundation of differential geometry. We will discuss the fundamental geometric objects (vector fields, tensor fields, differential forms) available on smooth manifolds and the basic operations dealing with such objects. We will also deal with integration on manifolds and Stokes theorem in the setting of manifolds with boundary. On the way we will discuss several applications of the techniques in areas between analysis and geometry, for example to Riemannian and symplectic geometry.

Assessment and permitted materials

Oral exam after the end of the course.

Minimum requirements and assessment criteria

Good knowledge of the central contents of the course as well as the ability to apply them in examples. The level of the course will follow the usual standards for master courses.

Examination topics

The contents of the course.

Reading list

Lecture notes for the course will be available online via http://www.mat.univie.ac.at/~cap/lectnotes.html and via moodle in due time. Depending on the way the course will be organized, I can provide additional material on moodle in the form of "informal remarks".
Examples for further literature:
J.M. Lee: "Introduction to smooth manifolds" (second edition), Graduate Texts in Mathematics 218, Springer 2013.
P.W. Michor: "Topics in Differential Geometry", Graduate Studies in Mathematics 93, Amer. Math. Soc. 2008.

Association in the course directory

MGED

Last modified: Fr 12.05.2023 00:21