Shamiur Rahman Ramim: A Gentle Introduction to Gröbner bases and Elimination Theory

Abstract: The main goal of this talk is to introduce the listener to the concept of a Gröbner basis for an ideal of a polynomial ring over a field (we will use C) and how these types of generating sets of ideals can be used to

1. determine if a system of polynomial equations has a solution,
2. determine the solutions of the system of polynomial equations in question.

This talk focuses on using Gröbner bases to solve the above problems. I will explain what Gröbner bases are, why they can be used to solve the above problems, and some general theory on the subject, but I will not show how to construct Gröbner bases. Instead, I will introduce the listener to the Macaulay2 computer algebra system and how to construct Gröbner bases with it. By doing so, I hope the listener is more inclined to use it for future problem solving.

For further details about the seminar, please check out our website . We are welcoming everyone that is interested.