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.
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The n-Category Café - University of Texas at Austin
5 days ago · 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.
The Riemann Hypothesis (Part 1) | The n-Category Café
Sep 7, 2019 · I’ve been trying to understand the Riemann Hypothesis a bit better. Don’t worry, I’m not trying to prove it — that’s a dangerous quest. Indeed Ricardo Pérez-Marco has a whole list of things not to do if you want to prove the Riemann Hypothesis, such as:. Don’t expect that the problem consists in resolving a single hard difficulty.
EGA1: The Language of Schemes | The n-Category Café
Feb 6, 2020 · Tim Hosgood, Ryan Keleti and others have finished an English translation of this classic:. Alexander Grothendieck, EGA1: The Language of Schemes and the LaTeX files are now open-source on GitHub. They are working on the rest of EGA, and they could use help!
Algebraic Closure | The n-Category Café - University of Texas at …
Apr 13, 2021 · Thanks for that — I had a much more complicated argument in mind, so I’m glad you came up with that simpler one. Here’s a variant on your example: splitting an idempotent is an example of a filtered colimit, and if you split the idempotent 0: ℤ → ℤ 0: \mathbb{Z} \to \mathbb{Z} in Ab Ab, you also get the trivial group.. The argument I had in …
Talk on the Tenfold Way | The n-Category Café - University of …
Feb 12, 2023 · Yes, the strong CP problem is very interesting. It’s a ‘problem’ if you believe, as most particle physicists do, that you need a good explanation for any renormalizable term that you can cook up from the fields in the Standard Model that’s missing from the Standard Model Lagrangian. I.e. just setting a coupling constant equal to zero without explanation counts as ‘cheating’ for them.
Borel Determinacy Does Not Require Replacement
Jul 23, 2021 · As you explicitly asked: In Etale cohomology of diamonds, I end up using beth-fixed points.(See Section 4; the somewhat weird conditions of Lemma 4.1 are equivalent to saying that κ \kappa is a beth fixed point of uncountable cofinality. When I wrote this section, I didn’t really know what I was doing…)
This Week's Finds (101--150) | The n-Category Café
Mar 7, 2023 · In Weeks 101–150 I focused strongly on topics connected to particle physics, quantum gravity, topological quantum field theory, and n n-categories.However, I digressed into topics ranging from biology to the fiction of Greg Egan to the game of Go.
August 2021 Archives | The n-Category Café - University of Texas …
Aug 30, 2021 · One of the most curious things about formal treatments of type theory is the attention paid to dummy variables. The point is simple enough to explain to a calculus student: just as the integrals ∫ 0 2 x 3 dx \int_0^2 x^3 \, dx and ∫ 0 2 t 3 dt \int_0^2 t^3 \, dt are equal, so are the functions λ x. x 3 \lambda x. x^3 and λ t. t 3 \lambda t. …