2013 Community Moderator Election

The community moderator election is currently in the nomination phase.

Please review and comment on the nominees by October 7!

Top new questions this week:

How do you not forget old math?

I am trying to not forget my old math. I finished my PhD in real algebraic geometry a few years ago and then switched to the industry for financial reasons. Now I get the feeling that I want to do a …

soft-question mathematics-education career real-algebraic-geometry

asked by Jose Capco 34 votes answered by fedja 30 votes

What is the amplituhedron?

The paper ”Scattering Amplitudes and the Positive Grassmannian” by Nima Arkani-Hamed, Jacob L. Bourjaily, Freddy Cachazo, Alexander B. Goncharov, Alexander Postnikov, and Jaroslav Trnka, introduces …

co.combinatorics mp.mathematical-physics grassmannians integrable-systems

asked by Gil Kalai 33 votes answered by Carlo Beenakker 15 votes

First occurrence of "by the usual compactness argument"?

In his blog, Jeff Shallit asks, what was the first occurrence of the exact phrase, "by the usual compactness arguments," in the mathematical literature? He reports that the earliest appearance he has …

reference-request exposition

asked by Gerry Myerson 18 votes answered by Moritz Firsching 20 votes

Intersection of compact sets in the unit interval

Let $\mathscr K$ be an uncountable set such that every $K\in\mathscr K$ is a compact subset of $[0,1]$ with positive Lebesgue measure. Does it then follow that there exists an uncountable $\mathscr …

set-theory gn.general-topology measure-theory real-analysis continuum-hypothesis

asked by TaQ 17 votes answered by Michael Renardy 17 votes

When is $f(x_1, \dots, x_n)+c$ an irreducible polynomial for almost all constants $c$?

Let $f\in \mathbb C[x_1, \dots, x_n]$, $n\ge 1$, be a non-constant polynomial. Consider the polynomial $f+t\in \mathbb C[t, x_1,\dots, x_n]$. This is an irreducible polynomial in $\mathbb C(t)[x_1, …

ag.algebraic-geometry ac.commutative-algebra polynomials

asked by Cantlog 15 votes answered by Michael Zieve 14 votes

Uniform proof that a finite reflection group is determined by its degrees?

Given a finite (real) group $G$ generated by reflections acting on euclidean $n$-space, it was shown by Chevalley in the 1950s that the algebra of invariants of $G$ in the associated polynomial …

gr.group-theory finite-groups coxeter-groups

asked by Jim Humphreys 13 votes

Letting $S(m)$ be the digit sum of $m$, then $\lim_{n\to\infty}S(3^n)=\infty$?

For any $m\in\mathbb N$, let $S(m)$ be the digit sum of $m$ in the decimal system. For example, $S(1234)=1+2+3+4=10, S(2^5)=S(32)=5$. Question 1 :Is the following true? …

nt.number-theory limits

asked by mathlove 13 votes answered by Vesselin Dimitrov 21 votes

Greatest hits from previous weeks:

Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture

Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville : “The big experts in the field had already tried to make this approach work,” Granville …

nt.number-theory prime-numbers

asked by pageman 67 votes answered by Mark Lewko 80 votes

Fourier vs Laplace transforms

In solving a linear system, when would I use a Fourier transform versus a Laplace transform? I am not a mathematician, so the little intuition I have tells me that it could be related to the boundary …

ca.analysis-and-odes fourier-analysis laplace-transform fourier-transform heuristics

asked by pirata 5 votes answered by Anweshi 6 votes

Can you answer these?

Souslin trees on the first inaccessible cardinal

This may be well-known or simply deducible from the existing theorems, but I didn't find an answer in my set theory books: Is there a model of $ZFC$ in which there are no $\kappa$-Souslin trees where …

lo.logic set-theory

asked by shahram 11 votes

About the ratio of the areas of a convex pentagon and the inner pentagon made by the five diagonals

Question : Letting $S{^\prime}$ be the area of the inner pentagon made by the five diagonals of a convex pentagon whose area is $S$, then find the max of $\frac{S^{\prime}}{S}$. I've been interested …

euclidean-geometry polyhedra

asked by mathlove 4 votes

Does this graph property have a name?

I'm interested in a family of properties of connected simple graphs that comes up in percolation theory. Let $G$ be a simple connected graph. Now consider the set of subgraphs of $G$ that I will call …

co.combinatorics graph-theory

asked by user40739 4 votes