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

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.

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.

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.

Jan 15, 2025 · We’re brought up to say that the dual concept of injection is surjection, and of course there’s a perfectly good reason for this. The monics in the category of sets are the injections, the epics are the surjections, and monics and epics are dual concepts in the usual categorical sense.

Feb 4, 2025 · This paper did it: Ruiyuan Chen, A universal characterization of standard Borel spaces, Journal of Symbolic Logic 88(2) (2023), 510–539. Here is his result: Theorem. The category SBor \mathsf{SBor} of standard Borel spaces and Borel maps is the (bi)initial object in the 2-category of countably complete countably extensive Boolean categories.. Here a category is countably complete if it has ...

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.

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 …

Jul 10, 2024 · guest post by Leonardo Luis Torres Villegas and Guillaume Sabbagh. Introduction. String diagrams are ubiquitous in applied category theory. They originate as a graphical notation for representing terms in monoidal categories and since their origins, they have been used not just as a tool for researchers to make reasoning easier but also to formalize and give algebraic semantics to previous ...

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.