Introduction of representation theory of finite groups (with some applications in algebraic geometry)

4-10 September 2023

Title of the course: Introduction of representation theory of finite groups (with some applications in algebraic geometry)
Instructor: Dr. Yulieth Prieto-Montañez
Institution: ICTP
Dates: 4-10 September 2023
Prerequisites: Linear algebra, algebra I (group theory)
Level: Graduate, advanced undergraduate
Abstract: One of the key goals of representation theory is to classify all possible representations of a given algebraic structure, such as a finite group. In this course, we will focus on studying and analyzing a comprehensive invariant known as the character, which plays a critical role in understanding and classifying representations. Since we are working with matrices, our initial approach is to consider matrix invariants. Particularly, we find that the trace is one of the main tools for effectively handling representations. To wrap up, the last lesson will be dedicated to practical applications in algebraic geometry.
Language: EN