Discriminant of Polynomials through the Lens of Galois Theory| Anasmit Pal | B.Math 2021-25

Title: Discriminant of Polynomials through the Lens of Galois Theory

Speaker: Anasmit Pal (B. Math, 3rd year)

Abstract: This talk explores the intricate relationship between discriminants and Galois groups of polynomials over a given field (mainly over Q). We begin by establishing foundational Galois theoretic concepts and theorems. Then, we delve into diverse methods for computing discriminants, including:

- Vandermonde matrices and Newton's Identities
- Resultants of Polynomials
- Norms of finite field extensions

We will also demonstrate how to compute Galois groups by analyzing cycle types of automorphisms within S_n.
This talk will be a very basic one with the pre-requisite being field theory, and will include lots of interesting examples.