Universität Wien
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877847 VO Differentialgeometrie und Lie Gruppen (2004S)

Topics in Differential Geometry and Lie Groups

0.00 ECTS (4.00 SWS), UG99 Mathematik

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Monday 01.03. 08:50 - 09:50 Seminarraum
  • Tuesday 02.03. 08:50 - 09:50 Seminarraum
  • Wednesday 03.03. 08:50 - 09:50 Seminarraum
  • Monday 08.03. 08:50 - 09:50 Seminarraum
  • Tuesday 09.03. 08:50 - 09:50 Seminarraum
  • Wednesday 10.03. 08:50 - 09:50 Seminarraum
  • Monday 15.03. 08:50 - 09:50 Seminarraum
  • Tuesday 16.03. 08:50 - 09:50 Seminarraum
  • Wednesday 17.03. 08:50 - 09:50 Seminarraum
  • Monday 22.03. 08:50 - 09:50 Seminarraum
  • Tuesday 23.03. 08:50 - 09:50 Seminarraum
  • Wednesday 24.03. 08:50 - 09:50 Seminarraum
  • Monday 29.03. 08:50 - 09:50 Seminarraum
  • Tuesday 30.03. 08:50 - 09:50 Seminarraum
  • Wednesday 31.03. 08:50 - 09:50 Seminarraum
  • Monday 19.04. 08:50 - 09:50 Seminarraum
  • Tuesday 20.04. 08:50 - 09:50 Seminarraum
  • Wednesday 21.04. 08:50 - 09:50 Seminarraum
  • Monday 26.04. 08:50 - 09:50 Seminarraum
  • Tuesday 27.04. 08:50 - 09:50 Seminarraum
  • Wednesday 28.04. 08:50 - 09:50 Seminarraum
  • Monday 03.05. 08:50 - 09:50 Seminarraum
  • Tuesday 04.05. 08:50 - 09:50 Seminarraum
  • Wednesday 05.05. 08:50 - 09:50 Seminarraum
  • Monday 10.05. 08:50 - 09:50 Seminarraum
  • Tuesday 11.05. 08:50 - 09:50 Seminarraum
  • Wednesday 12.05. 08:50 - 09:50 Seminarraum
  • Monday 17.05. 08:50 - 09:50 Seminarraum
  • Tuesday 18.05. 08:50 - 09:50 Seminarraum
  • Wednesday 19.05. 08:50 - 09:50 Seminarraum
  • Monday 24.05. 08:50 - 09:50 Seminarraum
  • Tuesday 25.05. 08:50 - 09:50 Seminarraum
  • Wednesday 26.05. 08:50 - 09:50 Seminarraum
  • Wednesday 02.06. 08:50 - 09:50 Seminarraum
  • Monday 07.06. 08:50 - 09:50 Seminarraum
  • Tuesday 08.06. 08:50 - 09:50 Seminarraum
  • Wednesday 09.06. 08:50 - 09:50 Seminarraum
  • Monday 14.06. 08:50 - 09:50 Seminarraum
  • Tuesday 15.06. 08:50 - 09:50 Seminarraum
  • Wednesday 16.06. 08:50 - 09:50 Seminarraum
  • Monday 21.06. 08:50 - 09:50 Seminarraum
  • Tuesday 22.06. 08:50 - 09:50 Seminarraum
  • Wednesday 23.06. 08:50 - 09:50 Seminarraum
  • Monday 28.06. 08:50 - 09:50 Seminarraum
  • Tuesday 29.06. 08:50 - 09:50 Seminarraum
  • Wednesday 30.06. 08:50 - 09:50 Seminarraum

Information

Aims, contents and method of the course

Geometry of classical symmetric spaces

1. Lobachevsky spaces.
Models, basic properties,
trigonometry, polyhedra, volumes.

2. Grassmannians.
Groups $\O(n)$.
Basic geometric structures. Coordinates.
Elements of geometry of angles (=complex distance).
Elements of topology.

3. Cartan domains U(p,q)/(U(p)x U(q)) and Sp(2n,R)/U(n).
Basic geometric structures.
Groups $\U(p,q)$ and $\Sp(2n,\R)$.
Krein-Schmullian category of linear relations and its properties.

4. Classical Lie groups and their finite dimensional representations.

5. General classical semisimple symmetric spaces.

Realizations.
Coordinates.
Matrix double ratio.
Overgroups of symmetries.

6. Hua densities. Inverse limits of classical groups and symmetric spaces.

7. Elements of geometry at infinity.
Symmetries of exterior algebras and Semple complexes.
Wonderful compactifications.
Satake--Furstenberg and Oshima--Sekiguchi boundary.
Tits building at infinity.

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

Reading list

Association in the course directory

Currently no association information is available.

Last modified: Mo 07.09.2020 15:50