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October 17, 2024
Associahedra in Quantum Field Theory
Posted by John Baez
I haven’t been carefully following quantum field theory these days, but some folks on the Category Theory Community Server asked me what I thought about recent work using the ‘amplitudohedron’ and other polytopes, so I decided to check out these videos:
- Nima Arkani-Hamed, Advanced class on amplitudes.
There are 5, and so far I’ve only finished watching the first. But I have to say: I enjoyed it more than any lecture on physics I’ve seen for a long time!
Arkani-Hamed has the amusing, informal yet clear manner of someone like Feynman or Coleman. And he explains, step by step, how imaginary particle physicists in some other universe could have invented the associahedra just by doing scattering experiments and looking for poles in the S-matrix. That blew my mind.
October 11, 2024
Axiomatic Set Theory 4: Subsets
Posted by Tom Leinster
Previously: Part 3
This phase of the course is all about building up the basic apparatus. We’ve stated our axioms, and it might seem like they’re not very powerful. It’s our job now to show that, in fact, they’re powerful enough to do just about everything with sets that mathematicians ever want. We began that job this week, with a chapter on subsets.
October 10, 2024
2-Rigs and the Splitting Principle
Posted by John Baez
We’re done!
- John Baez, Joe Moeller and Todd Trimble, 2-rig extensions and the splitting principle.
Our paper categorifies a famous method for studying vector bundles, called the ‘splitting principle’. But it also continues our work on representation theory using categorified rigs, called ‘2-rigs’. We conjecture a splitting principle for 2-rigs, and prove a version of it in the universal example.
But we also do more. I’ll only explain a bit, today.
October 4, 2024
Axiomatic Set Theory 3: The Axioms, Part Two
Posted by Tom Leinster
Previously: Part 2. Next: Part 4
This week, we finished formulating the axioms of the Elementary Theory of the Category of Sets.