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April 30, 2021
The Just Mathematics Collective
Posted by Tom Leinster
I recently learned of the Just Mathematics Collective, an “international collective of mathematicians” whose “goal is to shift the global mathematics community towards justice”.
It’s an ambitious initiative. We’ve had lots of discussions on this blog about specific places where the practice of mathematics meets real-world problems: surveillance of activist organizations, ties with violent armed groups, quandaries over funding, and so on. But JMC is looking at the big picture, encompassing all these issues and more. And the approach is nuanced: for example, rather than being crudely against the financial sector, it calls for a “reevaluation” of the relationship that we mathematicians have with it, also recognizing its potential for good.
Right now there’s a statement you can sign on the mathematical community’s ties with the NSA — the US National Security Agency, one of the world’s largest employers of mathematicians. You’ll probably find some familiar names on the list of signatories, including John Baez’s and mine.
April 20, 2021
Compositional Robotics
Posted by John Baez
A bunch of us are organizing a workshop on applications of category theory to robotics, as part of the IEEE International Conference on Robotics and Automation:
• 2021 Workshop on Compositional Robotics: Mathematics and Tools, online, 31 May 2021. Organized by Andrea Censi, Gioele Zardini, Jonathan Lorand, David Spivak, Brendan Fong, Nina Otter, Paolo Perrone, John Baez, Dylan Shell, Jason Kane, Alexandra Nilles, Andew Spielberg, and Emilio Frazzoli.
Submit your papers here by 21 May 2021!
Here’s the idea of the workshop….
April 16, 2021
Applied Category Theory 2021 — Call for Papers
Posted by John Baez
The deadline for submitting papers is coming up soon: May 12th.
- Fourth Annual International Conference on Applied Category Theory (ACT 2021), July 12–16, 2021, online and at the Computer Laboratory of the University of Cambridge.
Plans to run ACT 2021 as one of the first physical conferences post-lockdown are progressing well. Consider going to Cambridge! Financial support is available for students and junior researchers.
April 13, 2021
Algebraic Closure
Posted by Tom Leinster
This semester I’ve been teaching an undergraduate course on Galois theory. It was all online, which meant a lot of work, but it was also a lot of fun: the students were great, and I got to know them individually better than I usually would.
For a category theorist, Galois theory is a constant provocation: very little is canonical or functorial, or at least, not in the obvious sense (for reasons closely related to the nontriviality of the Galois group). One important not-obviously-functorial construction is algebraic closure. We didn’t get to it in the course, but I spent a while absorbed in an expository note on it by Keith Conrad.
Proving that every field has an algebraic closure is not entirely trivial, but the proof in Conrad’s note seems easier and more obvious than the argument you’ll find in many algebra books. As he says, it’s a variant on a proof by Zorn, which he attributes to “B. Conrad” (presumably his brother Brian). It should be more widely known, and now I find myself asking: why would you prove it any other way?
What follows is a somewhat categorical take on the Conrad–Zorn proof.