## June 18, 2024

### Magnitude Homology Equivalence

#### Posted by Tom Leinster

My brilliant and wonderful PhD student Adrián Doña Mateo and I have just arXived a new paper:

Adrián Doña Mateo and Tom Leinster. Magnitude homology equivalence of Euclidean sets. arXiv:2406.11722, 2024.

I’ve given talks on this work before, but I’m delighted it’s now in print.

Our paper tackles the question:

When do two metric spaces have the same magnitude homology?

We give an explicit, concrete, geometric answer for closed subsets of $\mathbb{R}^N$:

Exactly when their cores are isometric.

What’s a “core”? Let me explain…

## June 14, 2024

### 100 Papers on Magnitude

#### Posted by Tom Leinster

A milestone! By my count, there are now 100 papers on magnitude, including several theses, by a total of 73 authors. You can find them all at the magnitude bibliography.

Here I’ll quickly do two things: tell you about some of the hotspots of current activity, then — more importantly — describe several regions of magnitude-world that haven’t received the attention they could have, and where there might even be some low-hanging fruit.

## June 4, 2024

### 3d Rotations and the 7d Cross Product (Part 2)

#### Posted by John Baez

On Mathstodon, Paul Schwahn raised a fascinating question connected to the octonions. Can we explicitly describe an irreducible representation of $SO(3)$ on 7d space that preserves the 7d cross product?

I explained this question here:

This led to an intense conversation involving Layra Idarani, Greg Egan, and Paul Schwahn himself. The result was a shocking new formula for the 7d cross product in terms of the 3d cross product.

Let me summarize.