What is this?

This is an informal postdoc¹ circle for sharing skills and expertise in using M2-fu² towards research. The aims of this meeting are threefold:

• exchange specific examples of using M2 in forming conjectures and proving theorems.
• explore M2 roadblocks and bottlenecks that obstruct our research and discuss solutions.
• empower the community to understand and improve the core algorithms in M2.

This involves a mix of virtual gatherings, smaller one-on-one meetings, etc.

Macaulay2 is about research, not just programming!

We discuss research questions, M2 computations that led to them, and if there is a missing link, together we dive in to find the algorithmic problems and brainstorm ideas from different perspectives (e.g. start with an $F$-regularity question but end with contrasting algorithms for colon ideals.)

Potlucks are about community: everyone contributes!

Everyone uses M2 differently, depending on the unique computational aspects of their research area, therefore everyone is encouraged to pose a problem, example, or technique and open up a discussion. We will also practice contributing to Macaulay2 in ways that are in service of our research problems.

Collective does not mean a class or a debugging session!

Ultimately, the goal is to form a community of colleagues amongst whom collaborations can be born. When discussing a project, it will be communicated clearly whether or not it is open to collaborators or an ongoing project obstructed by computational questions which motivate a separate project.

Previous Meetings

August 26, 2025: Anna Brosowsky on $F$-purity and colon ideals

Anna talked about the problem of testing whether an ideal is $F$-Pure in positive characteristics + the Fedder’s criterion which uses colon ideals + the naive algorithm for computing colon ideals using intersection as a blackbox. Anna and collaborators are working on a project about F-purity of certain combinatorial ideals and posed the problem of effective testing of F-purity as a separate project.

After this, we used profile and profileSummary to investigate what pieces of code isFPure uses and split into three groups looking at:

• where intersection algorithms are in the Core
• where colon ideal algorithms are in the Saturation package
• where isFPure is implemented in TestIdeals package

I am intrigued! How do I join?

The next meeting will be late September/early October. In the meantime, send an email to mahrud@mcmaster.ca to be added to our Zulip channel.

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