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 2) | The n-Category Café
Oct 29, 2024 · Thurston’s paper Shapes of polyhedra and triangulations of the sphere is really remarkable. I’m writing about it in my next column for the Notices of the American Mathematical Society.Here’s a draft — which is also a much more detailed version of an earlier blog post here.
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.
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.
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 …
Axiomatic Set Theory 5: Relations | The n-Category Café
Oct 18, 2024 · Thanks for the kind words. And I do see your point. As you say, a definition is also just an agreement about how to use a word.. It’s also true that at the start of the course, I really wanted to emphasize to my students — undergraduates who’ve never done anything like this before — that everything has to come from the axioms, that nothing can be taken for granted.
The Icosahedron as a Thurston Polyhedron | The n-Category Café
Nov 5, 2024 · Here is Thurston’s procedure. First draw the lattice of Eisenstein integers in the complex plane: 피 = {a + b ω | a, b ∈ ℤ} \mathbb{E} = \{ a + b \omega \; \vert \; a, b \in \mathbb{Z} \} . where ω = exp (2 π i / 3) \omega = \exp(2 \pi i / 3).Then draw an 11-sided polygon P P whose vertices are Eisenstein integers. Along each edge of P …