Macaulay2: under the hood

The online seminar series "Macaulay2: under the hood" explores mathematical, algorithmic, and software issues behind the M2 software program. We hope to be accessible to a range of backgrounds, and all are welcome.

To sign up for the mailing list for the seminar click here: https://forms.gle/MVQ7yXLTgfZwM9YU6.

Upcoming:

1. Thursday January 30, 2025 at 9AM PDT, 10AM MST, 11AM CST, 12:00 PM EST, 17:00 GMT, 18:00 CET Speaker: Frank Moore.

Past events:

1. June 25, 2024 at 8:30 PDT, 10:30 CDT, 11:30 EDT, 16:30 BST, 17:30 CEST Speaker: Mike Stillman. Title: Introduction to the series

Abstract: This is the first talk in the “M2: under the hood” series. The idea of this series is to understand Macaulay2 in more depth; in particular, understand how its computations work, in order to be able to more effectively use Macaulay2. In this first talk, I will first describe the overall structure of the Macaulay2 system (the different parts: interpreter, engine, Core, packages, GitHub repository, git issues, and so on). After that, we will focus on one of the main computations in Macaulay2, computing free resolutions and minimal Betti numbers. We will provide an overview of the algorithm(s) used, the different ways one can call free resolutions, how they differ, and how Macaulay2 caches its results. We will also discuss how to speed up computations (if possible!) and how to deal with inhomogeneous and multi-graded input ideals or modules.

2. September 25, 2024 at 9AM PDT, 10AM MDT, 11AM CDT, 12:00 PM EDT, 17:00 BST, 18:00 CEST Speaker: Mike Stillman. Title: Free resolution algorithms

Abstract: In this talk, we will describe the mathematics behind the implementations of free resolutions in Macaulay2. In particular, the Schreyer resolution and its variations will be explored, including examples. 

3. November 13, 2024 at 9AM PDT, 10AM MST, 11AM CST, 12:00 PM EST, 17:00 GMT, 18:00 CET Speaker: Frank Moore. Title: Computing Gröbner Bases

Abstract: We will briefly recall the definition of Gröbner bases for ideals in a polynomial ring, and also mention extensions of this idea to several other instances. We will then discuss the standard algorithm for computing Gröbner bases, a linear algebra-based technique for reduction, as well as some optimizations of each. We will also address some pitfalls one may encounter when implementing these algorithms naively. Some attention will also be paid to discussing how one can use parallelism to decrease computation time.