Top new questions this week:

Grothendieck and DieudonnÃ© prove in $EGA_{II}$ (Proposition 5.5.5.(ii), page 105) that if $f:X\to Y, g:Y\to Z$ are projective morphisms of schemes and if $Z$ is separated and quasicompact, or if ...

Can monoids of endomorphisms of nonisomorphic groups be isomorphic ?

Let $(\Sigma_g, x)$ be a pointed topological surface of genus $g$, and let $MCG(g,1)$ be the mapping class group of this pointed surface. Then $MCG(g,1)$ has a natural action on $\pi_1(\Sigma_g, x)$ ...

This article describes the discovery by three physicists, Stephen Parke of Fermi National Accelerator Laboratory, Xining Zhang of the University of Chicago, and Peter Denton of Brookhaven National ...

The category $\text{AffSch}_S$ of affine schemes over some base affine scheme $S$ is not essentially small. This lends itself to certain settheoretical difficulties when working with a category ...

It is well known that if $M$ is a compact $n$dimensional manifold, then $[M, \mathbb{S}^n] \cong \mathbb{Z}$, i.e the maps are classified by their degree.
What is known about $[M, \mathbb{RP^n}]$ ...

Also posted on the Math Stackexchange: When is the number of areas obtained by cutting a circle with $n$ chords a power of $2$?
Introduction
Recently, a friend told me about the following ...

Greatest hits from previous weeks:

As a nonnative English speaker (and writer) I always had the problem of understanding the distinction between a 'Theorem' and a 'Proposition'. When writing papers, I tend to name only the main ...

What are the most important applications outside of mathematics of each of the major fields of mathematics? For concreteness, let's divide up mathematics according to arxiv mathematics categories, ...

I know of two good mathematics videos available online, namely:
Sphere inside out (part I and part II)
Moebius transformation revealed
Do you know of any other good math videos? Share.

There are some questions on mathoverflow such as
What outofprint books would you like to see reprinted?
Old books still used
with answers that tell us things such as:
Mathematicians prefer to ...

As I understand it, it has been proven that the axiom of choice is independent of the other axioms of set theory. Yet I still see people fuss about whether or not theorem X depends on it, and I don't ...

I am interested in magic tricks whose explanation requires deep mathematics. The trick should be one that would actually appeal to a layman. An example is the following: the magician asks Alice to ...

I am looking for mathematical documentaries, both technical and nontechnical. They should be "interesting" in that they present either actual mathematics, mathematicians or history of mathematics. I ...

Can you answer these questions?

Consider $(t, x)\in [0,T]\times (\mathbb{R}^d,d\mu)$, where the measure $d\mu(x)=K^{1}\exp(U(x))dx$ is a reasonable Gibbs measure (it satisfies a PoincarÃ© or logSobolev inequality. One can, for ...

I couldn't exactly guess the level of question. I asked in Math Stack Exchange. (Depending on the situation, I will remove it from here.)
I'm trying to understand a sketch of proof of Livingston and ...

$\underline {Background}$ : A coherent system on a polarized projective variety $(X, L)$ over $\mathbb C$ is a pair $(E,V)$, where $E$ is a $d$ dimensional coherent sheaf on $X$ and $V \subset H^0(E)$ ...
