AGQ: Representation Theory MATHS5094

  • Academic Session: 2024-25
  • School: School of Mathematics and Statistics
  • Credits: 15
  • Level: Level 5 (SCQF level 11)
  • Typically Offered: Either Semester 1 or Semester 2
  • Available to Visiting Students: No
  • Collaborative Online International Learning: No

Short Description

Broadly speaking, representation theory is the mathematical study of symmetries. The most successful physical theories which underpin our understanding of nature and new technologies rely on the algebraic description of symmetries. For example, the quantum fields in the standard model are governed by a representation of what physicists call a "gauge group", an algebraic structure which allows one to predict and find quantum particles. The mathematical study of representation theory can be seen as the attempt of classifying all possible manifestations of a group or symmetry and making them concrete in terms of matrices. While as a mathematical subject representation theory sits within the larger topic of algebra, it heavily draws on and influences other areas of mathematics such as geometry, combinatorics and number theory. Its application in physical theories has led to spectacular successes in making predictions and developing technologies. As such it is a core subject within the CDT training.

Timetable

2 hour sessions weekly.

The AGQ program will be setting the timing.

 

Classroom as well as equipment for online delivery to transmit the course to Edinburgh.

Requirements of Entry

This is a non-required course for students in the AGQ programme. With permission from AGQ directors students not enrolled in AGQ may also take this course.

Excluded Courses

none

Co-requisites

none

Assessment

Normally students will complete course work.

Course Aims

This course covers several fundamental topics in Representation Theory, providing a solid and broad foundation to the subject and its interactions with algebra and analysis. The course discusses representations of finite groups; symmetric groups (in detail), general linear groups, and finally the group SL(2) and its Lie algebra.

Intended Learning Outcomes of Course

On completion of this course, the student will be able to: • Thoroughly understand basic structures in representation theory of finite groups and general linear groups. • Solve problems involving characters, symmetries, complete reducibility.

Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.