Course Description

This course was offered online at the Indian Institute of Science,  Bangalore when I was an INSPIRE faculty at Harish-Chandra Research Institute, Prayagraj, India between 21 Mar, 2022--29 Jul, 2022. I want to thank Prof.  Sundaram Thangavelu  for the kind invitation.   I would also like  to thank Dr. Pritam Ganguly  and Dr. Rajesh Kumar Singh for recording my lectures. The aim of the course was to introduce Riemannian Symmetric Space to the audience.  Since the audience was diverse, I only assumed some basic knowledge of differential geometry and Lie groups as a prerequisite.

Syllabus

Classical Lie groups, Symmetric spaces:(Definition, examples, Generalities), Riemannian symmetric pair, Orthogonal symmetric Lie algebra, Classification and decomposition of Riemannian symmetric pair, Symmetric spaces of compact and non-compact type.

Lecture Note and Supplements

 Note,  Lec-8-supp.pdf, Lec-21-supp.pdf.

Lecture Video

Click here for the video link.

Reference

•  S. Helgason, "Differential geometry, Lie groups, and symmetric spaces", Academic press, 1979.

•  A. Borel, "Semi-simple Lie groups and Riemannian symmetric spaces", 1998.

• A. Iozzi,  "Lecture note on symmetric spaces",  Note.

• W. Ziller, "Lecture note on Lie groups, Representation theory, and Symmetric Spaces",  Note.