MATH 5010: Topics in Analysis I
Description: Advanced topics in analysis. With a change of content, this course is repeatable to a maximum of twelve credits.
MATH 5010 - Section 1: Topics in Analysis I
Description: This is an introduction to the theory of Lie groups, Lie algebras, and their representations. The course is intended for graduate students in mathematics and physics with little or no prior exposure to the Lie theory. We will focus on matrix Lie groups and Lie algebras to keep the exposition concrete. First we will look at the relationship between Lie groups and Lie algebras, along with basic representation theory. One of the main objects is the exponential map, and we will study its properties including the Baker-Campbell-Dynkin-Hausdorff formula. Then we will study root systems, and classification of semisimple Lie algebras. One of the possible goals of the course will be to show how the Lie theory is used in applications such as differential geometry and physics. The only prerequisite for taking the course is a background in linear algebra.
Prerequisites: MATH 5110.
Sections: Spring 2009 on Storrs Campus
|5010||1||Lecture||TuTh 12:30-1:45||MSB215||Gordina, Maria|