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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 :
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 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.