# AIS - Lie Groups and Lie Algebras (2023)

## Venue: Indian Institute of Science, Bengaluru

## Dates: 19 Jun 2023 to 8 Jul 2023

**Convener(s)**

Name: |
Apoorva Khare | R. Venkatesh |

Mailing Address: |
Associate Professor Department of Mathematics Indian Institute of Science Bangalore 560012 |
Assistant Professor Department of Mathematics Indian Institute of Science Bangalore 560012 |

Email: |
khare at iisc.ac.in | rvenkat at iisc.ac.in |

Lie groups and Lie algebras are one of the cornerstones of mathematics. They are well-studied in geometry, (harmonic) analysis, representation theory, number theory, string theory, and particle physics, to name several different fields – in addition to featuring in probability theory, control systems, and other areas. This AIS will focus on discussing and developing the basics of topological groups, Lie groups, and Lie algebras, with both their structure and their representations in mind.

The lectures aim to cover the basics of the structure theory of (complex semisimple) Lie algebras, root systems and Dynkin diagrams, topological and Lie groups, the Peter-Weyl theorem, and the correspondence between Lie algebras and Lie groups (via exponentiation). The lectures are meant for an audience of students and postdocs interested in Lie theory. Each lecture (in the morning) is accompanied by a tutorial session (in the afternoon).