Welcome to the Weekly Seminars on Gröbner bases and Applications. The weekly meetings will take place on Wednesdays 10:00-11:00 CE(S)T, at KU Leuven, campus Arenberg 3, in the seminar room B02.18 (full name 200B.02.018; second floor of the Math building 200B).
Organizers: Matthias Orth and Rafael David Mohr
Registration:
Please email Matthias if you are interested in attending the meeting or have any questions.
Overview:
The first goal of the seminar is to give an introduction to Gröbner bases and present some of their applications. Gröbner bases are one of the main tools underlying computer algebra systems such as Macaulay2 and Singular. This illustrates the central role they play for symbolic computation in Algebraic Geometry.
Schedule:
September 30, 2025 - 12:30 CEST - B02.18: Matthias Orth
Introduction to Gröbner bases: In this talk, I will define Gröbner bases and present the basic algorithm for computing them. I will give some context with regard to reduction relations, complexity, and non-commutative rings. We will also have time to discuss which topics to select for the more advanced part of the seminar- you are welcome to contribute ideas!
October 8, 2025 - 10:00 CEST - B02.18: Rafael David Mohr
First Applications of Gröbner bases using OSCAR: Following Matthias' introduction to Gröbner bases, I will present how their basic properties can be used in practice to solve problems coming from different areas of mathematics. For this I will show some concrete computations in the computer algebra system OSCAR which I plan to introduce briefly at the beginning of the session.
If you wish to follow along with the computations on your own computer you can find installation instructions for OSCAR here: https://www.oscar-system.org/install/linux/. At the top of the page you can find the instructions for different operating systems. If you encounter any issues during the installation feel free to contact me.
October 15, 2025 - 10:00 CEST - B02.18: Bence Sógor
Primary Decompositions: [Abstract TBA]
October 22, 2025 - 10:00 CEST - B02.18: Matthias Orth
Module Gröbner bases, syzygies, and free resolutions: [Abstract TBA]
October 29, 2025 - 10:00 CET - B02.18: Maria Agustina Cagliero
Weight vectors, homogenization, and the Gröbner fan, part 1: [Abstract TBA]
November 5, 2025 - 10:00 CET - B02.18: Daniel Windisch
Weight vectors, homogenization, and the Gröbner fan, part 2: [Abstract TBA]
Books:
Ideals, Varieties and Algorithms by David A. Cox, John Little and Donal O'Shea
Using Algebraic Geometry by David A. Cox, John Little and Donal O'Shea