Aug 15, 2024 · Galois Theory Posted by Tom Leinster. I’ve just arXived my notes for Edinburgh’s undergraduate Galois theory course, which I taught from 2021 to 2023.. I first shared the notes on my website some time ago. But it took me a while to arXiv them, because I wanted to simultaneously make public most of the other course materials.

Oct 31, 2024 · The quantum computation topic, and mentor, have changed to this: Structuring Quantum Effects with Monads and Arrows. Mentor: Juliana Kaizer Vizzotto Category theory provides a mathematical framework for understanding structures and their relationships abstractly.

Oct 26, 2024 · I’m writing a short column about this paper: W. P. Thurston, Shapes of polyhedra and triangulations of the sphere. Let me describe one of the key ideas as simply as I can.

Dec 4, 2024 · Submission Important dates . All deadlines are AoE (Anywhere on Earth). February 26: title and brief abstract submission; March 3: paper submission

3 days ago · Next: Part 2 In this post and the next, I want to try out a new idea and see where it leads. It goes back to where magnitude began, which was the desire to unify elementary counting formulas like the inclusion-exclusion principle and the simple formula for the number of orbits in a free action of a group on a finite set.

Oct 17, 2024 · 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, …

2 days ago · I hope you’ve read the news: Ethan Singer, Thousands of U.S. government web pages have been taken down since Friday, New York Times, 2 Feburary 2025. Many of the pages taken down mention DEI, but they also include research papers on optics, chemistry, medicine and much more.

Jul 20, 2024 · Those other quantities are important, but they’re not called ‘temperature’. They’re called the ‘thermodynamic conjugates’ of the conserved quantities in question. I haven’t heard people discuss the thermodynamic conjugate of angular momentum or momentum, but Landau uses these (perhaps implicitly—I forget) to argue that an object in …

Aug 25, 2024 · Very nice! It’s pleasing to find a real-world interpretation to motivate otherwise obscure calculations. Regarding the point at the end, about how the standard Central Limit Theorem doesn’t imply pointwise convergence of densities, the keyword for the kind of result you need is “local limit theorem”.Here

Nov 22, 2024 · Previously: Part 9. The course is over! The grand finale was the theorem that. X × Y ≅ X + Y ≅ max (X, Y) X \times Y \cong X + Y \cong max(X, Y) . for all infinite sets X X and Y Y.Proving this required most of the concepts and results from the second half of the course: well ordered sets, the Cantor–Bernstein theorem, the Hartogs theorem, Zorn’s lemma, and so on.