Special Math Lecture： Groups and their representations

Aim of the course

Group theory plays an important role in many fields, as for example in quantum mechanics or in particle physics. During this one semester course, we shall introduce the main concepts of groups, their representations, and present some classical groups. Lie groups and Lie algebras will also be discussed.

Prerequisites

A basic knowledge on calculus and linear algebra is expected, as provided for example in Calculus I & II and in Linear algebra I & II. For that reason, motivated 1st year students can attend this course but only after a discussion with the instructor.

Course contents

1. Groups
2. Linear representations
3. Lie groups
4. Semisimple theory

Evaluation methods

The final grade will be determined by the active participation during the lectures (will be explained during the first lecture).

Notice for students

This course is an optional subject which does not count towards the number of credits required for graduation in any program at Nagoya University.

Additional information

http://www.math.nagoya-u.ac.jp/~richard/SMLspring2018.html

Textbook

Material will be provided during the lectures

Reference Book

Reference books will be provided during the lectures

http://www.math.nagoya-u.ac.jp/~richard/teaching/s2018/Notes_groups.pdf

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