## Top new questions this week:

### Is it worthwhile to give off-topic talks?

I am a graduate student. Occasionally for some reason I am asked to give a talk on my research at a conference whose stated purpose is almost completely unrelated to my research. To preserve my …

soft-question career

### Does Fermat's last theorem hold in the ordinals?

My question is whether there are no nontrivial solutions in the ordinals of the equations arising in Fermat's last theorem $$x^n+y^n=z^n$$ where $n\gt 2$, and where we use the natural ordinal …

set-theory diophantine-equations
 asked by Joel David Hamkins 23 votes

### In any Lie group with finitely many connected components, does there exist a finite subgroup which meets every component?

This question concerns a statement in a short paper by S. P. Wang titled “A note on free subgroups in linear groups" from 1981. The main result of this paper is the following theorem. Theorem (Wang, …

gr.group-theory lie-groups

### The exponent of Ш of y^2 = x^3 + px, where p is a Fermat prime

For $d$ a non-zero integer, let $E_d$ be the elliptic curve $$E_d \colon y^2 = x^3+dx.$$ When we let $d$ be $p = 2^{2^k}+1$, for $k \in \{1,2,3,4\}$, sage tells us that, conditionally on BSD,  \# …

nt.number-theory elliptic-curves tate-shafarevich-groups

### Verlinde's formula

"Verlinde's formula" predicts the dimension of the space of conformal blocks of a chiral CFT. Depending on... • which chiral CFT one considers (does one restrict to WZW models, or not?) …

ag.algebraic-geometry reference-request conformal-field-theory vertex-algebras

### Counting 2m X 2m 0-1 matrices with m ones in each row and each column.

Given $m>1$, what is the number of $2m\times 2m$ matrices, made of $0$ and $1$, such that each row has exactly $m$ ones, and each column has exactly $m$ zeros. I am not sure if this is a …

co.combinatorics

### A function composed with itself produces the identity

Let $B$ be the closed unit ball in $\mathbb R^3$ and $f: B\to B$ continuous, such that $f\circ f$ is the identity (i.e., $f\circ f=\mathbb 1_B$) and $f$ restricted on $\partial B$ is also the identity …

gt.geometric-topology gn.general-topology involutions

## Greatest hits from previous weeks:

### Linear Algebra Texts?

Can anyone suggest a relatively gentle linear algebra text that integrates vector spaces and matrix algebra right from the start? I've found in the past that students react in very negative ways to …

books big-list ra.rings-and-algebras linear-algebra

### Why is differentiating mechanics and integration art?

It is often said that "Differentiation is mechanics, integration is art." We have more or less simple rules in one direction but not in the other (e.g. product rule/simple <-> integration by …

ca.analysis-and-odes real-analysis integration

## Can you answer these?

### Equiareal shapes in $\mathbb{R}^d$

There was quite a bit of work on the so-called equichordal problem throughout the 20th century, to decide if some plane convex curve could have two equichordal points. A point is equichordal for a …

mg.metric-geometry

### List of cubical spaces

Suppose I have a three-dimensional cube (I tend to think of it as a regular ideal cube in $\mathbb{H}^3,$ but you don't have to). I glue up its sides in some way to obtain topological spaces. The …

gt.geometric-topology