# Symmetric Spaces Spring 2020

Lecturer
Prof. Dr. Marc Burger
Coordinator
Raphael Appenzeller, (mail)

## Content

Possible topics include:
• Locally and globally Symmetric Spaces
• Symmetric Spaces from the differential geometric viewpoint
• Symmetric Spaces from the Lie groups viewpoint
• Cartan decomposition
• Decomposition in compact/non-compact/Euclidean factors
• Duality theory
• Flats and rank
• Root space decomposition
• Iwasawa decomposition
• Examples
Vorlesungsverzeichnis

## Coronavirus-Precautions

To allow a smooth continuation we provide you with the following ressources:

## Prerequisites

Some basic knowledge of differential geometry and Lie groups.

## Exercises

New exercises and solutions will appear here approximately every two weeks. If you hand in your solution, you will get the corrected exercises back. Please scan your solutions and send them via mail to "raphael.appenzeller@math.ethz.ch". Doing exercises is an essential part of any lecture.

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exercise sheet due by solutions
Exercise sheet 1 Friday 13.3.2020 Solutions 1
Exercise sheet 2 Friday 27.3.2020 Solutions 2
Exercise sheet 3 Friday 17.4.2020 Solutions 3
Exercise sheet 4 Friday 1.5.2020 Solutions 4
Exercise sheet 5 Friday 21.5.2020 Solutions 5
Exercise sheet 6 Friday 5.6.2020 Solutions 6

## Schedule

Lectures (V) and exercise classes (U) take place on Tuesday and Thursday.

Tuesday 10-12 a.m. HG F26.5, HG G 43 (Hermann Weyl Zimmer) at homeThursday 8-10 a.m. HG F26.5 HG G 43 (Hermann Weyl Zimmer) at home
18.2. V20.2. V
25.2. V27.2. V
3.3. V 5.3. U
10.3. V 12.3. V - Video recording
17.3. V - Video recording 19.3. U - Video recording
24.3. V - Video recording 26.3. V - Video recording
31.3. V - Video recording 2.4. U - Recording and notes
7.4. V - Video recording 9.4. V - Video recording
break break
21.4. V - Video recording 23.4. U V - Video recording
28.4. V - technical problems (no recording) 30.4. V - Video recording
5.5. V - Video recording 7.5. U V - Video recording
12.5. V U - Recording and notes 11.5. V - Video recording; 12.5. V - Video recording
18.5. V - Video recording 22.5. V - Video recording
26.5. Recap with RA, Notes and recording 28.5. Recap with RA, Notes and recording

## Literature

References for Riemannian geometry:
• M. Berger, "A panoramic view of Riemannian geometry", Springer, 2003
• W.M. Boothby, "An Introduction to Differentiable manifolds and Riemannian Geometry', Elsevier 1986
• M.P. do Carmo, "Riemannian Geomtrey", Birkhauser, 1992
References for symmetric spaces: