Programa de Doutorado 2012:Lie Groups, Representation Theory and Symmetric Spaces

Part I: In the first part, we discuss geometric properties of Lie groups and Lie algebras including the classification of semisimple Lie algebras (root space decomposition and Dynkin diagrams).

Part II: In the second part we cover the basics of representation theory of semisimple Lie algebras and of compact Lie groups.

In both cases, a geometric view point will be emphasized, applying algebraic properties of the Lie algebra to geometric properties of the underlying Lie group. In part II we will e.g. discuss both real and complex representations of compact Lie groups as an application of the usual theory of complex representations of complex semisimple Lie algebras.

Part III: If time permits, we will also discuss the theory of symmetric spaces, which are basic examples not only in geometry, but in many areas of mathematics. Unlike Helgason, the basic reference for the subject, the emphasis will be on the geometric aspects as opposed to algebraic ones.

 

Vídeos

Lie Groups, Representation Theory and Symmetric Spaces

Wolfgang Ziller

Aula 01 - 12.03.2012 - download

Aula 02 - 14.03.2012 - download

Aula 03 - 19.03.2012 - download

Aula 04 - 21.03.2012 - download

Aula 05 - 02.04.2012 - download

Aula 06 - 04.04.2012 - download

Aula 07 - 09.04.2012 - download

Aula 08 - 11.04.2012 - download

Aula 09 - 13.04.2012 - download

Aula 10 - 16.04.2012 - download

Aula 11 - 18.04.2012 - download

Aula 12 - 25.04.2012 - download

Aula 13 - 30.04.2012 - download

Aula 14 - 02.05.2012 - download

Aula 15 - 04.05.2012 - download

Aula 16 - 07.05.2012 - download

Aula 17 - 09.05.2012 - download

Aula 18 - 14.05.2012 - download

Aula 19 - 16.05.2012 - download

Aula 20 - 21.05.2012 - download

Aula 21 - 23.05.2012 - download

Aula 22 - 28.05.2012 - download

Aula 23 - 30.05.2012 - download

Aula 24 - 04.06.2012 - download

Aula 25 - 06.06.2012 - download

Aula 26 - 11.06.2012 - download

Aula 27 - 13.06.2012 - download

Aula 28 - 18.06.2012 - download

Aula 29 - 20.06.2012 - download

Aula 30 - 25.06.2012 - download

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