John C. Baez's Blog, page 21

Talk on the Tenfold Way

There are ten ways that a substance can have symmetry under time reversal, switching particles and holes, both or neither. But this fact turns out to extend far beyond condensed matter physics! It’s really built into the fabric of mathematics in a deep way.

Next Monday I’m giving a talk about this. It’s at 10 am Pacific Time, or 18:00 UTC. To attend, you need to register here. You can see my slides already here.

Mathematics for Humanity

We discussed this here earlier, but now it’s actually happening!

The International Centre for Mathematical Sciences, or ICMS, in Edinburgh, will host a new project entitled ‘Mathematics for Humanity’. This will be devoted to education, research, and scholarly exchange having direct relevance to the ways in which mathematics can contribute to the betterment of humanity. Submitted proposals will be reviewed on April 15, 2023.

The activities of the program will revolve around three interrelated ...

Topos Institute Positions

The Topos Institute is doing some remarkable work in applying category theory to real-world problems. And they’re growing!

They want to hire a Finance and Operations Manager and a Research Software Engineer. For more information, go here.

And if you’re a grad student working on category theory, you definitely want to check out their summer research positions! For more information on those, go here. Applications for these are due February 15th, 2023.

A Curious Integral

On Mathstodon, Robin Houston pointed out a video where Oded Margalit claimed that it’s an open problem why this integral:

is so absurdly close to but not quite equal.

They agree to 41 decimal places, but they’re not the same!

while

So, a bunch of us tried to figure out what was going on.

Jaded nonmathematicians told us it’s just a coincidence, so what is there to explain? But of course an agreement this close is unlikely to be “just a coincidence”. It might be, but you’ll never get anywh...

Guillotine Partitions and the Hipparchus Operad

If you dissect a square into n similar rectangles, what proportions can these rectangles have? Folks on Mathstodon figured this out for n ≤ 7, and I blogged about it here recently. But I was left feeling that some deeper structure governed this problem.

Various people on Mathstodon, including Steven Stanicki, David Eppstein and Rahul Narain, convinced me of the importance of a certain class of dissections called ‘guillotine partitions’. I started suspecting that these were connected to an op...

Dividing a Square into Similar Rectangles

If you divide a square into some fixed number of similar rectangles, what proportions can these rectangles have? We’ve been having fun thinking about this on Mathstodon, and here is a report.

If you divide a square into 3 similar rectangles, what proportions can these rectangles have? There are three options. The third is more complicated than the first two:

• We can divide the square into three rectangles that are 1/3 as long in one direction as the other, as in the first picture.

• We ca...

Free Idempotent Rigs and Monoids

I’ve been having a lot of fun on Mathstodon lately, and here’s an example.

A rig R has a commutative associative addition, an associative multiplication that distributes over addition, an element 0 with r+0 = r and for all r ∈ R and an element 1 with 1r = r = r1 for all r ∈ R

A rig is idempotent if r r = r for all r ∈ R.

Is the free idempotent rig on 2 generators finite? If so, how many elements does it have?

Morgan Rogers raised this issue on the Category Theory Community server, and after a ...

Adjoint School 2023

Are you interested in applying category-theoretic methods to problems outside of pure mathematics? Apply to the Adjoint School!

Apply here. And do it soon.

• January 9, 2023. Application Due.

• February – July, 2023. Learning Seminar.

• July 24 – 28, 2023. In-person Research Week at University of Maryland, College Park, USA

Participants are divided into four-person project teams. Each project is guided by a mentor and a TA. The Adjoint School has two main components: an online learning semin...

ACT 2023

Here’s a bit of information about the conference Applied Category Theory 2023, and the associated Adjoint School—a school on applied category theory.  Many students have gotten into applied category theory by attending this school!

They will both take place at the University of Maryland in College Park, Maryland. Here are the dates:

• Adjoint School: July 24–28, 2023.
• Applied Category Theory conference: July 31–August 4, 2023.

Applications for the Adjoint School are due January 9, 2023. You c...

This Week’s Finds – Lecture 10

This Thursday is the last of my lectures on This Week’s Finds… until they resume next September. As usual we’ll meet in Room 6206 of the James Clerk Maxwell Building, home of the Department of Mathematics of the University of Edinburgh. And as usual you can attend via Zoom:

https://ed-ac-uk.zoom.us/j/82270325098
Meeting ID: 822 7032 5098
Passcode: Yoneda36

Later a video of the talk will appear on my YouTube channel.

I’ll talk about quaternions in physics and Dyson’s ‘three-fold way’: the way t...