Galois Theory | The n-Category Café - University of Texas at Austin
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.
Triangulations of the Sphere (Part 1) | The n-Category Café
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.
Stirling's Formula from Statistical Mechanics | The n-Category Café
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
Associahedra in Quantum Field Theory | The n-Category Café
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, …
ACT 2025 | The n-Category Café
Dec 4, 2024 · Submission Important dates . All deadlines are AoE (Anywhere on Earth). February 26: title and brief abstract submission; March 3: paper submission
Adjoint School 2025 | The n-Category Café
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.
Martianus Capella | The n-Category Café
Dec 10, 2024 · John, thank you for the overview. I think two points might be of interest. It seems that reluctance to accept heliocentric theory was not only due to the resistance from the church (which undoubtedly existed), but also because the Copernican system quickly led to the predictions that were very difficult to reconcile with the available observations.
Bernoulli Numbers and the Harmonic Oscillator
Aug 16, 2024 · Alas, Pierre Cartier died on Saturday, August 17th, 2024. Anyone who never met him should watch this interview of him, in French with English subtitles. It really gets across his personality. For some of his thoughts related to “mathemagics”—that is, math using mysterious formal manipulations—go to 48:32.Great expression on his face when he describes how Bourbaki’s negative attitude ...
What Is Entropy? | The n-Category Café - University of Texas at …
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 …
Overview of the general case 1 The generalized McShane’s identity gives a formula for the length L1 of a pre-specified boundary component 1 of X 2Mg; n(L1;:::;L ) as a sum of terms over all pants containing 1. 2 We integrate this formula over moduli space Mg;n(L1;:::;Ln) using Mirzakhani’s integration formula which gives us an integral in …