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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.

Posted at 9:53 PM UTC | Permalink

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….

Posted at 5:00 PM UTC | Permalink | Post a Comment

April 16, 2021

Applied Category Theory 2021 — Call for Papers

Posted by John Baez

The deadline for submitting papers is coming up soon: May 10th.

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.

Posted at 2:45 PM UTC | Permalink | Post a Comment

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.

Posted at 12:13 PM UTC | Permalink | Followups (20)

March 31, 2021

Can We Understand the Standard Model Using Octonions?

Posted by John Baez

I gave two talks in Latham Boyle and Kirill Krasnov’s Perimeter Institute workshop Octonions and the Standard Model.

The first talk was on Monday April 5th at noon Eastern Time. The second was exactly one week later, on Monday April 12th at noon Eastern Time.

Here they are…

Posted at 10:20 PM UTC | Permalink | Followups (33)

March 29, 2021

Native Type Theory (Part 3)

Posted by John Baez

guest post by Christian Williams

In Part 2 we described higher-order algebraic theories: categories with products and finite-order exponents, which present languages with (binding) operations, equations, and rewrites; from these we construct native type systems.

Now let’s use the wisdom of the Yoneda embedding!

Posted at 4:57 AM UTC | Permalink | Followups (35)

March 21, 2021

Native Type Theory (Part 2)

Posted by John Baez

guest post by Christian Williams

We’re continuing the story of Native Type Theory.

In Part 1 we introduced the internal language of a topos. Now, we describe the kinds of categories TT from which we will construct native type systems, via the internal language of the presheaf topos 𝒫T\mathscr{P}T.

Posted at 1:55 AM UTC | Permalink | Followups (5)

March 18, 2021

A Group Theory Problem

Posted by John Baez

Preparing a talk on octonions and the Standard Model, I’m struggling with a calculation in this paper:

and I’d like your help. The essence of the problem is nothing about octonions, it’s about Lie groups — and pretty simple Lie groups too, like SU(2)\mathrm{SU}(2) and SU(3)\mathrm{SU}(3). So, there’s a good chance you can help me out. I’ll explain it.

Posted at 11:52 PM UTC | Permalink | Followups (27)

March 17, 2021

Can We Understand The Standard Model?

Posted by John Baez

I’m giving a talk in Latham Boyle and Kirill Krasnov’s Perimeter Institute workshop Octonions and the Standard Model on Monday April 5th at noon Eastern Time.

This talk will be a review of some facts about the Standard Model. Later I’ll give one that says more about the octonions.

Posted at 2:45 AM UTC | Permalink | Followups (20)

Mathematics in the 21st Century

Posted by John Baez

I’m giving a talk in the Topos Institute Colloquium on Thursday March 25, 2021 at 18:00 UTC. I believe that’s 11:00 am Pacific Time. In any event, that’s when I plan to show up.

As usual for them, it will be broadcast live on Zoom and also on YouTube, where it will be recorded for posterity. Only Zoom lets you ask questions. The password for Zoom can be found on the Topos Institute Colloquium website.

Posted at 2:34 AM UTC | Permalink | Followups (1)

March 14, 2021

Emerging Researchers in Category Theory

Posted by John Baez

Eugenia Cheng is an expert on giving clear, fun math talks.

Now you can take a free class from her on how to give clear, fun math talks!

You need to be a grad student in category theory, and priority will be given to those who aren’t at fancy schools, etc.

Her course is called the Emerging Researchers in Category Theory Virtual Seminar, or Em-Cats for short. You — or some student you know! — can apply for it here:

The first round of applications is due April 30th. It looks pretty cool, and knowing Eugenia, you’ll get a lot of help on giving talks.

Posted at 10:00 PM UTC | Permalink | Post a Comment

March 8, 2021

Parametric adjoints = multi-adjoints

Posted by Mike Shulman

Here are two “weakenings” of the notion of adjoint functor:

  1. If CC has a terminal object 11, a functor F:CDF:C\to D is a parametric right adjoint if the induced functor F 1:CD/F1F_1 : C \to D/F 1 is a right adjoint.

  2. A functor F:CDF:C\to D has a left multi-adjoint if for each yDy\in D there is a (small) family of morphisms {η y,i:yFx i} iI\{ \eta_{y,i}:y \to F x_i\}_{i\in I} such that for any morphism g:yFzg:y\to F z, there is a unique pair of an index iIi\in I and a morphism h:x izh:x_i \to z such that g=Fhη y,ig = F h \circ \eta_{y,i}.

I just noticed that these two definitions are almost exactly the same! Specifically, if CC has a terminal object and DD is locally small, then a functor F:CDF:C\to D is a parametric right adjoint if and only if it has a left multi-adjoint.

Posted at 4:40 PM UTC | Permalink | Followups (14)

March 2, 2021

Postdoctoral Position in Higher Category Theory at Johns Hopkins University

Posted by Emily Riehl

The Department of Mathematics at Johns Hopkins University solicits applications for one two-year postdoctoral fellowship beginning Summer 2021 (with some flexibility in the start and end dates). The position is funded by the Army Research Office (ARO) through the Multidisciplinary University Research Initiative (MURI) program. This position is open to anyone who is able to obtain a visa to come and work in the US, but it is necessary to be physically in the US to receive funding from this grant. (Johns Hopkins will sponsor and pay for a visa application, if required.)

The nn-Category Café has recently hosted a lively discussion on the ethics of military funded mathematics and US military funding in particular. This is the first time I’ve collaborated on a military funded grant, so I have limited experience in this area. But every year, I’m heartbroken to disappoint the dozens of highly-qualified postdoctoral applicants I come in contact with. My department also offers university-funded postdoctoral positions (though one could argue that military funding provides some support for all employees at Johns Hopkins) but at some point I calculated that it would be “my turn” to make an offer to my first choice candidate exactly once a decade, and I wanted to try to find a way to hire others in the meanwhile.

Posted at 7:35 PM UTC | Permalink | Post a Comment

Funding of the nLab

Posted by David Corfield

The nLab was born out of conversations at the Café back in 2008. Over the past 12 years it has grown as a wiki to over 15000 pages.

For many years it was funded personally by Urs Schreiber, until in the last few years when it relied on a fund kindly provided by Steve Awodey.

But now we have new arrangements in place, and are looking to its users to help fund the nLab:

In 2021, the nLab will move to the cloud. To fund the running of the nLab in the cloud, we have decided to rely upon funding by donations. In the autumn of 2020, at the kind initiative of Brendan Fong, the nLab decided to collaborate with the Topos Institute for the practical side of this: the Topos Institute is legally able to handle donations, and the financing of the nLab will be handled by the Topos Institute. The Topos Institute owns the cloud account in which the nLab will be run.

Please do consider making a donation here.

Posted at 7:38 AM UTC | Permalink | Followups (5)

March 1, 2021

Theoretical Physics in the 21st Century

Posted by John Baez

I’m giving a talk at the Zürich Theoretical Physics Colloquium next Monday, for Sustainability Week 2021. I’m excited to get a chance to speak both about the future of theoretical physics and the climate crisis. You can attend if you want.

Posted at 10:26 PM UTC | Permalink | Post a Comment