Notices by John Carlos Baez (johncarlosbaez@mathstodon.xyz)

Someone wrote:

"Please give a step by step plan for someone wishing to pursue a career in applied category theory."

Someone replied:

"Okay, here is a step-by-step plan for someone wishing to pursue a career in Applied Category Theory (ACT). This field is relatively niche and often interdisciplinary, so the path requires both strong theoretical foundations and a focus on practical application domains.

Phase 1: Foundational Knowledge (Undergraduate Level & Early Grad School/Self-Study)

Step 1: Master Core Mathematics:

Calculus & Linear Algebra: Essential building blocks for almost all quantitative fields. Ensure a deep, conceptual understanding.

Discrete Mathematics: Crucial for logic, proofs, graph theory, combinatorics – many areas where ACT finds application.

Abstract Algebra: Groups, rings, fields, modules. Understanding algebraic structures is fundamental before generalizing with categories. Homomorphisms are precursors to functors.

Set Theory & Mathematical Logic: Understand the foundations upon which mathematics, including category theory, is built. Formal proofs are essential.

(Optional but Recommended) Point-Set Topology: Introduces concepts like continuity and open sets in an abstract way, which have categorical analogues (e.g., limits, colimits).

(1/n)

Looking to leave the US? If you're a mathematician, consider a career in the winelands area of South Africa! Stellenbosch is hiring!

The Mathematics Division at Stellenbosch University in South Africa is looking to hire a new permanent appointment at Lecturer / Senior Lecturer level. Other levels may be considered too under the appropriate circumstances.

Preference will be given to candidates working in number theory or a related area, but those working in other areas of mathematics will definitely also be considered.

The closing date for applications is 30 April 2025. For more details, kindly see the official advertisement:

https://mcusercontent.com/ff8bceee86d2e6e23e78dc57c/files/761fb0d7-424a-d674-0107-1b84dfc23387/NW080630325_Senior_Lecturer_Lecturer_Dept_of_Mathematical_Sciences_Web_Copy_2_.pdf

In 2019 Carole Cadwalladr gave a TED talk that broke from their tradition of glowing techno-optimism. She told the world about the Facebook-Cambridge Analytica scandal. She was met with a lot of anger, and she got sued.

Now she's back with a talk about the "digital coup" in the US. I'll just quote a lot of the transcript.

...

I have a lot of emotions about coming here. And TED, also, I suspect, is feeling them too. But what actually I finally realized yesterday is that the denial and the confusion that I've been feeling is maybe what you're feeling, too.

I felt powerless for a really long time. So if that's what you're feeling, I get it. But we have to act now. My alarm system is ringing again. There are things that we can do. In my case, I survived. And you will too. But it's by learning how to fight back. This is my guide, and it has to start with naming it. It's a coup.

I know you probably don't want to hear that, and especially here, but we can’t fight it if we can’t see it. And we can’t see it if we don’t name it.

The Russian and American presidents are now speaking the same words. They are telling the same lies. We are watching the collapse of the international order in real time. And this is just the start.

Coups are like concrete. When they stop moving, they set. It is already later than we think.

(1/n)

https://www.youtube.com/watch?v=TZOoT8AbkNE

Platinum is a silver-colored metal with a high melting point. If you heat it to 3825 °C, it will boil! If you carefully study platinum vapor, you can see spectral lines - different colors of light - as the electrons hop from one energy level to another.

Inside a platinum atom there's a nucleus. This too has different energy levels, shown in the middle picture. The energies here are huge: about 1 million electron volts. So, as the nucleus hops from one energy level to another, it emits gamma rays.

Physicists have come up with many theories that try to predict these energy levels. At left we see predictions of a theory called the SO(6) DS model. DS stands for 'dynamical symmetry' and SO(6) is a group of symmetries. The predictions are not *completely* wrong, but they're damned bad. At right are predictions of a more complicated theory called the SO(6) 'partial dynamical symmetry' model. They're better, though still flawed.

I'm studying these theories not because I care about the energy levels of platinum nuclei, but because it's incredibly cool that symmetry groups like SO(6) have anything to do with nuclear physics! Why? Because SO(6) is the group of rotations in 6-dimensional space!

What in the world does 6-dimensional space have to do with platinum nuclei? Here's what:

A platinum nucleus in its lowest energy level is shaped roughly like a kiwi fruit: an ellipsoid with all 3 axes of different length. In higher energy levels this ellipsoid is vibrating, constantly changing shape back and forth. It takes 6 numbers to describe an ellipsoid. So, we can describe the nucleus with a point in 6 dimensional space, which vibrates back and forth.

(1/2)

Now the gloves come off.

In the simplest theory of oscillating ellipsoids, all 6 numbers describing an ellipsoid are treated equally, so we get a harmonic oscillator in 6 dimensions. This has SO(6) symmetry due to rotations in 6d space. But the phase space of this harmonic oscillator is not ℝ⁶ but ℂ⁶, with complex coordinates describing both the position *and momentum* of the oscillator! In fact the oscillator has U(6) symmetry, due to unitary transformations of ℂ⁶. The group U(6) is a lot bigger than SO(6). Yum!

In this simplest possible theory we want a Hamiltonian that's invariant under U(6). The usual Hamiltonian for a quantum harmonic oscillator has this property. Indeed, U(6) acts on the Hilbert space of the 6d quantum harmonic oscillator, so the Casimir of U(6) gives an invariant operator on this Hilbert space... and this works out to be the harmonic oscillator Hamiltonian!

But suppose we want a more realistic yet still tractable theory. One way is to say our theory only needs to have SO(6) symmetry. Then we get another possible term in the Hamiltonian: the Casimir for SO(6). Or we can admit our theory only needs to have SO(3) symmetry, due to rotations in physical 3d space. This suggests another possible term: the Casimir for SO(3).

In the SO(6) SD model, the Hamiltonian is a linear combination of 3 terms:

• the Casimir for SU(6)
• the Casimir for SO(5)
• the Casimir for SO(3)

For more details, check out the paper where I got the picture:

• J.E. Garcia-Ramos, A. Leviatan, P. Van Isacker, Partial dynamical symmetry in quantum Hamiltonians with higher-order terms, https://arxiv.org/abs/0812.4109

I'm still puzzled by the geometry involved... these guys ignore that.

(2/2)

How are international conferences dealing with the fact that some people are now afraid or unwilling to enter the US? Are they holding conferences elsewhere, encouraging remote participation, ignoring the issue, or what?

If you're helping run an international conference (like me), or even just going to one, I'd like to know what you're seeing.

https://www.science.org/content/article/international-scientists-rethink-us-conference-attendance

Some atomic nuclei are round. Others are football-shaped. Some are even stranger. Some are pear-shaped! Some have a 'halo' of protons and neutrons orbiting a smaller core. They're all just minimizing energy - unless they're in a temporary 'excited state'. But the forces between protons and neutrons are so complex that this can make lots of things happen.

Just as noble gases are exceptionally inert because they have a filled shell of electrons, the roundest and most stable nuclei are those with a filled shell of protons - and, separately, a filled shell of neutrons. Filled shells happen when we hit a 'magic number'. The magic numbers are

2, 8, 20, 28, 50, 82, and 126.

I want to show you some cool patterns in these numbers. But first, some examples:

• Hydrogen, with just one proton, is perfectly round, but that's an exception.

• Helium-4 has 2 protons and 2 neutrons, and that's the second most common element in the universe.

• Oxygen-16 has 8 protons and 8 neutrons, and this is the most common form of oxygen.

• Calcium-40 has 20 protons and 20 neutrons, and this is the most common form of calcium. It's also the heaviest stable nucleus that has the same number of protons and neutrons! Heavier nuclei need more neutrons to be stable, but calcium-40 is stabilized by the fact that 20 is a magic number.

• Calcium-48 has 20 protons and 28 neutrons. It's not stable, because it has too many neutrons - but it has a half-life of 64 quintillion years, so it's damned close to being stable, thanks to the power of magic numbers.

• Lead-208 has 82 protons and 126 neutrons. It's the most common form of lead.

(1/2)

In nuclear physics, the magic numbers are

  2
  8 = 2+6
 20 = 2+6+12
 28 = 2+6+12+8
 50 = 2+6+12+8+22
 82 = 2+6+12+8+22+32
126 = 2+6+12+8+22+32+44

What's the big deal about this? I could explain it to you, but I'm just learning this stuff, so I'd basically be repeating the explanation here:

https://en.wikipedia.org/wiki/Nuclear_shell_model

The basic idea is this: neutrons and protons in nuclei form 'shells' somewhat like how electrons form shells in atoms... so a lot of the same math applies, namely the representation theory of the rotation group. But protons and neutrons interact so strongly that the patterns get complicated, even for fairly small nuclei. For the electrons in atoms, we can do surprisingly well at predicting the patterns in the periodic table by pretending they don't interact, until we reach rather large atoms.

(2/2)

When he took office, Trump signed an executive order declaring a national emergency at the U.S.–Mexico border. He also directed Defense Secretary Pete Hegseth and Homeland Security Secretary Kristi Noem to provide a report within 90 days about the state of the border to determine “whether to invoke the Insurrection Act of 1807.”

That means April 20th.

When it's invoked, the Insurrection Act gives the president the authority to deploy the U.S. military or National Guard inside the country to suppress events such as rebellion, insurrection and civil disorder. It provides an exception to the Posse Comitatus Act of 1878, which limits the use of military personnel under federal command for law enforcement within the US.

If you think this is unlikely, don't forget that the Trump gang fired the nation’s top uniformed officer and also the top uniformed lawyers at the Army, Navy and Air Force, all of whom would probably put breaks on reckless actions like this.

So, it's time to learn about the Insurrection Act:

https://en.wikipedia.org/wiki/Insurrection_Act_of_1807

It can be activated in 3 ways, and the 2 most likely now are:

• to address an insurrection, in any state, which makes it impracticable to enforce the law

or

• to address an insurrection, domestic violence, unlawful combination or conspiracy, in any state, which results in the deprivation of constitutionally secured rights, and where the state is unable, fails, or refuses to protect said rights

The article here talks about some people wargaming scenarios for what happens if Trump invokes the Insurrection act, and also some things we can do if he does:

https://truthout.org/articles/what-should-we-do-if-trump-invokes-the-insurrection-act/

Another one bites the dust! The editorial board of the journal Mathematical Logic Quarterly have resigned en masse, complaining about the publisher, Wiley:

"The managing editors and editors of MLQ believe that the academic editorial process guaranteeing scientific quality control should be entirely in the hands of an editorial team consisting of members of the academic research community that are entirely free from pressure or influence of commercial and profit-oriented interests."

They've started a new journal of mathematical logic that's "diamond open access". This means simply that it's free to publish in and free to read.

Because they're German, they decided to call this new journal Zeitschrift für Mathematische Logik und Grundlagen der Mathematik. But they'll forgive you if you call it ZML:

https://blog.tib.eu/2025/04/07/mlq-walk-out/

This move is part of a trend. The Open Access Tracking Project now lists more than 200 articles on such "declarations of independence":

https://tagteam.harvard.edu/hubs/3/tag/oa.declarations_of_independence

If you're on an editorial board, you should want to convert your journal to diamond open access. And there are resources to help you do it:

https://www.openaccess.nl/en/diamond-open-access/resources
https://toolsuite.diamas.org/

People are desperately rushing to save data from the National Oceanic and Atmospheric Administration (NOAA) before their Amazon Web Services go dead tonight... thanks to DOGE. That's a lot of weather and climate data.

The thread continues:

"Help very much needed. Some tips…

Instructions for scraping from SciOp
If you begin working on an archive, please mention that you’ve claimed it in a reply to this thread and then edit your reply with an update when it’s completed and/or uploaded
If you archive a resource but can’t upload it to SciOp, that’s okay, just let us know
Possible third-level domains based on certificate issuances (thank you, @jenniferplusplus)
Possible sites/datasets based on the master NOAA github account (thank you, @Catladylilia)"

If you want to help, go to the Safeguarding Research & Culture website:

https://forum.safeguar.de/t/noaa-all-services-specifically-amazon-web-servies-urgent/569

and read the whole thread, then sign up.

I hope you join me in demonstrating against the authoritarian takeover - Saturday April 5th!

I found a great list of events you can go to, better than the one I shared before:

https://www.mobilize.us/handsoff/

Yes, there's a protest happening here in Riverside California! But they're happening all over. I read 514,000 people have signed up for protests on the Indivisible webstite. I bet a bunch more people ain't signing up, just going.

Want to leave the US? Stockholm University is also hiring an Assistant Professor in Mathematics with focus on Mathematical Logic in the Department of Mathematics. The position is tenure track and the candidate will be part of the long standing tradition of logic research in Stockholm. Applicants from all areas of logic and related areas are very welcome to apply. Women and other underrepresented groups are strongly encouraged to apply.

Application deadline: April 15, 2025, 11:59 PM CEST

The Logic group in Stockholm currently consists of professor emeritus Per Martin-Löf and associate professors Peter LeFanu Lumsdaine and Anders Mörtberg with PhD students and postdocs. The Department is a vibrant place for logic research with a weekly seminar (https://logic.math.su.se/seminar/), advanced courses in logic, and close collaborations with other research groups in Sweden and internationally.

More information about the position and how to apply: https://su.varbi.com/en/what:job/jobID:796743/where:4/

(2/2)

Want to leave the US? The University of Sussex is paying a theoretical computer science grad student for 3.5 years to do a PhD. This is is available to UK and international applicants.

You'd be doing research with Philip Saville on denotational semantics using categories and 2-categories. You'd receive:

a tax-free stipend at the standard rate for 3.5 years- currently £20,780 per year for 25/26

a fee waiver at the UK or international rate for 3.5 years

a one-off Research and Training Support Grant of £2,000

The project description starts:

"The project will be in the field of denotational semantics, a branch of theoretical computer science in which one builds mathematical models of programming languages. Such models are used in many ways. For example, might answer questions about program behaviour: one can show that no program exists with a certain behaviour, or understand how programs with complex collections of features -- such as probability, looping, and exceptions -- ought to behave. Alternatively, by studying models of programs we can understand the mathematical structure of programs, and thereby discover new language paradigms or constructs.

Just as physics draws on mathematics, and can lead to mathematical results in its own right, so denotational semantics often intersects with deep and interesting mathematical ideas. The project will use the powerful language of category theory to build new models and study the relationships between existing ones. In particular, it will likely make use of 2-dimensional category theory and category-theoretic universal algebra."

You can see more details here:

https://www.sussex.ac.uk/study/fees-funding/phd-funding/view/1840-PhD-Informatics-Studentship:-Denotational-semantics-via-(2-dimensional)-categories

My cousin Joan is 84, but she's still got it going on. Here's how she kicked off the first episode of John Mulaney's comedy talk show.

(I think someone had asked her about Martin Luther King's sense of humor.)

https://www.thedailybeast.com/joan-baez-derails-john-mulaneys-live-show-to-attack-trump/

If you have a valid visa to be in the US, be very careful. The Trump gang is starting to deport, detain, and perhaps even torture people in your situation! Here are some examples:

Dr. Rasha Alawieh is a kidney specialist working at Brown University. After visiting family in Lebanon, she was returning to the U.S. on an H-1B visa - a temporary visa that lets foreign professionals work in the US - when customs officials detained her at the airport in Boston. A federal court order was issued to stop her deportation. But she was deported anyway, sent off on a plane to Lebanon!

https://www.patriotledger.com/story/news/2025/03/16/rhode-island-doctor-rasha-alawieh-deported-despite-federal-court-order/82466816007/

(1/n)

Fabian Schmidt is a lawful permanent resident of the US, but he too was detained by immigration officers at the same airport in Boston - Logan Airport. He had been visiting Luxembourg, and flew back to the U.S. on Friday. His partner had gone to pick him up at Logan Airport, and waited four hours before calling authorities.

His mother says Schmidt was “violently interrogated” for hours at the airport, stripped naked, put in a cold shower by two officials, and being put back onto a chair.

She said Schmidt told her immigration agents pressured him to give up his green card. She said he was placed on a mat in a bright room with other people at the airport, with little food or water, suffered sleep deprivation, and was denied access to his medication for anxiety and depression.

“He hardly got anything to drink. And then he wasn’t feeling very well and he collapsed,” said Senior.

He was transported by ambulance to Mass General Hospital. Then he was transported to the regional headquarters for ICE in Burlington, Massachusetts, and then transferred to the Wyatt detention facility in Boston. Lawyers are attempting to get him out.

https://www.nhpr.org/nh-news/2025-03-14/green-card-holder-from-new-hampshire-interrogated-at-logan-airport-detained

(2/n)

This is a somewhat different case. Tourists from Germany can generally visit the US for up to 90 days without a visa. But this one, Lucas Sielaff, made the mistake of driving to Tijuana, Mexico with his partner to get medical treatment for her dog. When they came back, he had trouble understanding the border control officer questioning him. He gave a muddled answer and got taken to an interrogation room.

After more than an hour of questioning, he was denied re-entry to the U.S. and was chained to a bench along with other travelers.

Outside, his partner was trying to get answers from officials. In response, she says, they searched her car. When she raised objections, two ICE officers detained her and took her to a separate room, where she was subjected to a humiliating body search.

“For the first time in my life, I’m in handcuffs,” she said. “As they’re walking me into a building, they’re twisting my arms.”

After the body search, she, too, was chained to a bench for a time before being released.

Lucas Sielaff was held at the border post for two more days, sleeping on a bench under a Mylar blanket, and then transferred to the Otay Mesa Detention Center. For two weeks, he shared a cell with eight other people. Eventually he was deported on a flight that cost him $2,744.

Something similar happened to another German tourist to the US, Jessica Brösche. She too made the mistake of going to Mexico and trying to get back into the US. She was held for 46 days.

https://www.10news.com/news/team-10/it-is-like-jail-german-man-visiting-american-fiance-detained-by-ice-for-over-2-weeks

(3/n)

And then there are hundreds of Venezuelans who were sent to the "Terrorism Confinement Center", a massive prison in El Salvador - even though a federal judge ordered that the planes reverse course and return the detainees to the United States!

The right-wing president of El Salvador, Nayib Bukele, made a joke of it on social media: “Oopsie … Too late.” And his post was recirculated by the White House communications director, Steven Cheung. So they are completely mocking the judicial system.

“This sure looks like contempt of court to me,” said David Super, a law professor at Georgetown University. “You can turn around a plane if you want to.”

Paywalled: https://www.nytimes.com/2025/03/16/us/constitutional-crisis.html

Free to read here: https://archive.is/2lXvG

(4/n)

Another case - I'm not keeping up with all of them:

Becky Burke, from Wales, was halfway through a backpacking trip across North America when ICE grabbed her and detained her for 19 days. She is now back in Wales. Her parents haven't asked her for many details yet, but they say she was "taken in leg chains, waist chains and handcuffs".

ICE says she violated "the terms and conditions of her admission". Her parents guess maybe it was because she was on a tourist visa and she'd been getting free lodging from people on her trip in exchange for helping them around the house... thus violating her tourist visa, which doesn't allow employment???

It raises lots of questions.

https://www.bbc.com/news/articles/cly67j35y99o

(4/n)