MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

The coupon collector's earworm

I thank Nicolas Dupont for the following question (and for permission to disseminate it further): I have a playlist with, say, $N$ pieces of music. While using the shuffle option (each such ...

reference-request co.combinatorics asymptotics  
asked by Noam D. Elkies 27 votes
answered by Kevin P. Costello 11 votes

Why should we care about "higher infinities" outside of set theory?

Let's say you are a prospective mathematician with some addled ideas about cardinality. If you assumed that the natural numbers were finite, you'd quickly vanish in a puff of logic. :) If you ...

set-theory soft-question  
asked by Cosmonut 22 votes
answered by Joel David Hamkins 21 votes

Which algebraic relations are possible between algebraic conjugates?

For which non-constant rational functions $f(x)$ in $\mathbb{Q}(x)$ is there $\alpha$, algebraic over $\mathbb{Q}$, such that $\alpha$ and $f(\alpha) \neq \alpha$ are algebraic conjugates? More ...

nt.number-theory polynomials  
asked by Gabriel Dill 16 votes
answered by GNiklasch 14 votes

A Linear Order from AP Calculus

In teaching my calculus students about limits and function domination, we ran into the class of functions $$\Theta=\{x^\alpha (\ln{x})^\beta\}_{(\alpha,\beta)\in\mathbb{R}^2}$$ Suppose we say that ...

co.combinatorics ct.category-theory real-analysis order-theory linear-orders  
asked by Dmitry V 15 votes

Brouwer's theorem for the Cauchy reals

Brouwer famously proved, using principles motivated by intuitionistic choice sequences, that every function $\mathbb{R}\to \mathbb{R}$ is continuous. In Sheaves in geometry and logic (section VI.9), ...

ct.category-theory topos-theory constructive-mathematics sheaves  
asked by Mike Shulman 12 votes
answered by aws 4 votes

Which sequential colimits commute with pullbacks in the category of topological spaces?

This question was asked on math.stackexchange.com without a reaction. Given diagrams of topological spaces $$X_0\rightarrow X_1\rightarrow\ldots$$ $$Y_0\rightarrow Y_1\rightarrow\ldots$$ ...

at.algebraic-topology ct.category-theory gn.general-topology  
asked by user78499 12 votes
answered by Philippe Gaucher 0 votes

How big is the lattice of all functions?

Define the lattice $(\mathcal{L},\prec)$ as the set of all function $f:\mathbb{N}\rightarrow\mathbb{N}$ satisfying $f(n)\leq f(n+1)\leq f(n)+1$, where two functions are considered equal if they differ ...

reference-request lattice-theory  
asked by Jan-Christoph Schlage-Puchta 11 votes
answered by Dominic van der Zypen 4 votes

Greatest hits from previous weeks:

Good programs for drawing graphs ( directed weighted graphs )

Does anyone know of a good program for drawing directed weighted graphs?

graph-theory software  
asked by dan 20 votes
answered by William Stein 21 votes

Video lectures of mathematics courses available online for free

It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some ...

ho.history-overview mathematics-education soft-question big-list  
asked by alex 224 votes
answered by Charles Siegel 40 votes

Can you answer these?

Detecting torsion-classified bundles by differential invariants

The following is based on a loose understanding of the nuts and bolts that go into Chern-Simons theory, so bear with any vagueness on my part. Suppose I have a principal $G$-bundle $P\to M$ and I ...

dg.differential-geometry principal-bundles  
asked by David Roberts 5 votes

Indecomposable representations of a wreath product

If $G$ is a finite group, we know the irreducible representations of $G ≀ S_n$ (over $\mathbb Q$) are classified by partitions of $n$ 'decorated' by an irrep of $G$. I'm wondering to what extent the ...

gr.group-theory rt.representation-theory  
asked by Kevin Casto 5 votes

Tangent space of Hilbert scheme

We have the following theorem: Let $X$ be a projective scheme over an algebraically closed field $k$, and $Y \subset X$ a closed subscheme with Hilbert polynomial $P$. Then$$T_{[Y]}\text{Hilb}_P (X) ...

ag.algebraic-geometry  
asked by user78628 7 votes
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