SUPERIOR ALGEBRA 2
cod. 1010206

Learning objectives

The students will learn the basic definitions, problems, and techniques in Representation Theory.

Prerequisites

Algebra (groups, rings, fields); Linear Algebra.
The course “Algebra Superiore 1” is NOT a prerequisite.

Course unit content

Representation Theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory.
The course is meant as an introduction to Representation Theory. In the first part, we will discuss the basics of the theory and introduce the fundamental problems. In the second part, we will study in detail the representation theory of finite groups, in particular symmetric groups, with their character theory.

Full programme

- - -

Bibliography

[E] P. Etingof et al., Introduction to representation theory.
[FH] W. Fulton, J. Harris, Representation Theory. A first course.

Both books are freely available online.

Teaching methods

The topics of the course will be discussed during the lectures, together with examples, applications, and exercises. Attendance is highly recommended.

Assessment methods and criteria

At the end of the course there will be an exam at the board, where the student will be asked to solve an exercise and discuss, explain, and prove one of the main results of the course.

Other information

The courses of “Algebra Superiore 1” and “Algebra Superiore 2” are completely independent. However, they are complementary. The attendance of both courses may be beneficial, and it is strongly recommended.

2030 agenda goals for sustainable development