Universität Wien
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250096 VO Analysis on manifolds (2020S)

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

  • Tuesday 03.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 10.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 17.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 24.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 26.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 31.03. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.04. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.04. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.04. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.04. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.04. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 05.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 12.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 14.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 19.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 26.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.05. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 04.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 18.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 25.06. 09:45 - 11:15 Hörsaal 11 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 30.06. 09:45 - 11:15 Hörsaal 11 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 basic 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. In the end of the course, we will discuss several applications of the techniques in areas between analysis and geometry, for example basics of symplectic and contact geometry.

For the period of home learning, students are expected to study the material following the lecture notes. The moodle page for the course containes detailes information on the material that should be studied, additional texts on parts of the lecture notes and a forum, in which students can pose questions and initiate discussions.

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

For example:
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.
some lecture notes will be made available online at http://www.mat.univie.ac.at/~cap/lectnotes.html in due time.

Association in the course directory

MGED

Last modified: Fr 19.02.2021 11:48