Spring 2026
Daniel Ketover
Course Description:
An introduction to Lie groups and Lie algebras.
Text:
Introduction to smooth manifolds (Lee) and Compact Lie groups (Sepanski)
Prerequisites:
undergraduate topology and analysis
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Spring 2025
Chris Woodward
Course Description:
The introductory level will introduce students to basic ideas in Lie groups and Lie algebras, which are useful for application within Lie theory and in other parts of mathematics, such as algebra, geometry, topology, and number theory.
Text:
None required, but we will use the chapters from Lee's "Smooth Manifolds" and some material from Brocker tom Dieck's GTM "Representations of Compact Lie Groups"
Prerequisites:
Undergraduate topology and analysis
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Spring 2024
Vladimir Retakh
Course Description:
An introduction to Lie groups
Text:
W. Fulton, J. Harris, Representation Theory. A First Course.
Prerequisites:
Undergraduate topology and analysis
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Spring 2023
Christopher Woodward
Course Description:
An introduction to Lie groups
Text:
Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics, 5) by Wulf Rossmann (Author) 4.9 out of 5 stars 6 ratings ISBN-13: 978-0199202515 ISBN-10: 0199202516
Prerequisites:
Undergraduate topology and analysis
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Spring 2022
Christopher Woodward
Course Description:
An introduction to Lie groups and Lie algebras
Text:
Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics, 5) by Wulf Rossmann (Author) 4.9 out of 5 stars 6 ratings ISBN-13: 978-0199202515 ISBN-10: 0199202516
Prerequisites:
Undergraduate topology and analysis
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Spring 2021 - Siddhartha Sahi
Course Description:
This will be a highly _individualized_ course covering topics in Lie groups. I will teach this course at two levels, and students can pick the level appropriate to their background, training, and interest. The introductory level will introduce students to basic ideas in Lie groups and Lie algebras, which are useful for application within Lie theory and in other parts of mathematics, such as algebra, geometry, topology, and number theory. This level will be collaborative in nature. The advanced level will be more individualized, where I will help each student choose a topic in Lie theory appropriate to his/her taste. I will explain the main ideas in some recent research work in that area (perhaps, but not necessarily, my own!), suggest generalizations, and possible lines of attack. We will discuss this over the course of the semester, with the aspirational goal of having some *new* mathematics by the end of the semester. In particular, if you took "Lie groups" last time, there need be no overlap!
Text:
None
Prerequisites:
Basic graduate courses
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Schedule of Sections