# Tag Info

### Why do Grothendieck topologies used in algebraic geometry typically involve finiteness conditions?

To give an interesting data point, I can offer two examples of something that seems a bit more infinitary. If we consider the category of finite-dimensional manifolds, and covers being submersions (or ...
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### Golden ratio in contemporary mathematics

Let $\rho$ be the binary substitution defined by: $$\rho(00)=\text{empty word}\quad\rho(01)=1\quad\rho(10)=0\quad\rho(11)=01.$$ Let $R$ be the self-map of $[0,1]$ associating to every $x=(0.w)_2$ the ...
1 vote

### Golden ratio in contemporary mathematics

Golden ratio appeared in the recent breakthrough of Frankl's Union Closed Set conjecture by Justin Gilmer, as well as the subsequent optimization of the lower bound constant. It relies crucially on ...

### Good "casual" advanced math books

Since no one has mentioned this I found the following trilogy by Ash and Gross fits your description: Fearless Symmetry , Elliptic Tales and Summing It Up. I personally had enjoyed reading them and ...
1 vote

### Good "casual" advanced math books

I'm surprised that no one has yet mentioned The Symmetries of Things by John Conway, Heidi Burgiel and Chaim Goodman-Strauss. It's ostensibly an introduction to symmetry groups but touches into ...

### Has the mathematical content of Grothendieck's "Récoltes et Semailles" been used?

Yes, R&S proved to be influential in at least one sense, the mathematical work of Z. Mebkhout (part four is dedicated to him indeed: "À Zoghman Mebkhout l’ouvrier solitaire en témoignage de ...

### What are some very important papers published in non-top journals?

Graph minors. II. Algorithmic aspects of tree-width The seminal graph minors papers of Robertson and Seymour were mostly published in JCTB (one of the top discrete maths journals). But this paper, ...
1 vote

### Shapes for category theory

A limit of an idempotent (viewed as a diagram whose shape is the "idempotent category") is a splitting of the idempotent. This cannot be expressed using directed graphs as shapes I think.
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