Inculcation: Lie groups, symmetric spaces and beyond

introductory §

• Lie Groups and Lie Algebras - YouTube
• Borcherds - Lie groups - YouTube
• Introduction to Lie Theory
• Short course on Lie Groups by M.S. Raghunathan - YouTube

Lie groups and Lie algebras §

• Introduction to Lie Groups (Fall 2020, ETHz)（部分）_哔哩哔哩_bilibili
  • https://metaphor.ethz.ch/x/2020/hs/401-3225-00L/
• Unitary Representations of Lie Groups | ETH Zürich Videoportal
  • Unitary | Books
• Anupam Singh - AIS on Lie Algebras (4-23 July 2011) CMI-IMSc, Chennai (google.com)
  • CMI Lie algebras - YouTube
• Introduction to Lie Algebras Doutorado IMPA Verao 2011 Reimundo Heluani 03/01/2011 aula 01 parte1 (youtube.com)
• AIC - Compact Lie groups and their representations (2022)- Prof. M. S. Raghunathan, Centre for Basic Sciences, Mumbai - YouTube
  • AIC - Compact Lie groups and their representations (2022)
  • notes

Lie groups and symmetric spaces §

• A guide through the theory of symmetric spaces
• Programa de Doutorado: Lie Groups, Representation Theory and Symmetric Spaces - YouTube
• Muna Naik - Riemannian Symmetric Space
  • Riemannian Symmetric Spaces - an introduction (Muna Naik)
• Homogeneous Dynamics and Geometry in Higher-Rank Lie Groups - YouTube
• Geometry, Groups and Dynamics (GGD) - 2017 | ICTS

broader topics §

• Harish-Chandra & Centenary Celebrations at HRI
  • Syllabus
• The year-long program on Harish-Chandra’s birth centenary - YouTube
  • Harish-Chandra Lectures series at Bhaskaracharya Pratishthana and IISER Pune
• Discrete subgroups of Lie groups - YouTube
• Rigidity - FRH - YouTube
  • there’s some notes in Alp Uzman’s Webpage
• Nigel Higson: Parabolic induction - YouTube
• Nigel Higson: Real reductive groups, K-theory and the Oka principle - YouTube
• Fields Academy Shared Graduate Course: Automorphic Forms and Representation Theory: an introduction to the Langlands Program | Fields Institute for Research in Mathematical Sciences

Geometric representation theory §

• Borel–Weil–Bott theorem - Wikipedia
• Raphaël Rouquier - Geometric representation theory as representation-theoretic geometry (youtube.com)
• Geometric Representation Theory_哔哩哔哩_bilibili
• Workshop on Representation Theory and Geometry - YouTube
• Hodge theory & Unitary representations - YouTube

symplectic geometry and representation theory §

• HIM Lectures: Trimester Program “Symplectic Geometry and Representation Theory” - YouTube

ergodic theory and Lie groups §

• Uri Bader: course in groups and ergodic theory in Wroclow - YouTube

Banach algebras, C*-algebras §

• Harmonic Analysis and Banach Algebras. A. Pirkovskii. Fall 2024. - YouTube
• C* algebras and spectral theorem - YouTube
• C* Algebra Course Lecture_哔哩哔哩_bilibili
• A. Yu. Pirkovskii. C*-algebras and compact quantum groups. Spring 2021 - YouTube
• C*-Algebras and Compact Quantum Groups. Pirkovskiy A. Y. Spring 2024 - YouTube
• K-Theory of C*-Algebras (2025) - YouTube