## Top new questions this week:

### Can you give an example of two projective morphisms of schemes whose composition is not projective?

Grothendieck and Dieudonné 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 quasi-compact, or if ...

ag.algebraic-geometry counterexamples projective-morphisms

### Monoids of endomorphisms of nonisomorphic groups

Can monoids of endomorphisms of nonisomorphic groups be isomorphic ?

gr.group-theory semigroups-and-monoids

### Are these local systems on $\mathscr{M}_{g,1}$ motivic?

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 $\pi_1(\Sigma_g, x)$ ...

ag.algebraic-geometry gt.geometric-topology mapping-class-groups

### Consequences of eigenvector-eigenvalue formula found by studying neutrinos

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 ...

linear-algebra matrix-analysis matrix-theory

### Surmounting set-theoretical difficulties in algebraic geometry

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

### Homotopic classification of maps $M \to \mathbb{RP}^n$ where $M$ is a compact $n$-dimensional manifold

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 $[M, \mathbb{RP^n}]$ ...

at.algebraic-topology homotopy-theory

### When is the number of areas obtained by cutting a circle with $n$ chords a power of $2$?

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 ...

nt.number-theory co.combinatorics discrete-geometry

## Greatest hits from previous weeks:

### Theorem versus Proposition

As a non-native 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 ...

soft-question mathematical-writing

### Real-world applications of mathematics, by arxiv subject area?

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, ...

applications mathematics-education popularization big-list

### Best online mathematics videos?

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.

soft-question big-list examples online-resources

### Old books you would like to have reprinted with high-quality typesetting

There are some questions on mathoverflow such as What out-of-print books would you like to see re-printed? Old books still used with answers that tell us things such as: Mathematicians prefer to ...

soft-question big-list books latex

### Why worry about the axiom of choice?

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 ...

lo.logic set-theory axiom-of-choice

### Magic trick based on deep mathematics

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 ...

soft-question big-list popularization

### Interesting mathematical documentaries

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

soft-question big-list

## Can you answer these questions?

### Trace and second-order inverse trace on space with Gibbs measure

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 Poincaré or log-Sobolev inequality. One can, for ...

fa.functional-analysis pr.probability ap.analysis-of-pdes sobolev-spaces

### Boundary of slice disk exterior is the zero surgery of slice knot

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 ...

gt.geometric-topology knot-theory
 asked by Diego Hernández Rodríguez 1 vote

### On simplicity of $q$ stable coherent systems

$\underline {Background}$ : 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 $V \subset H^0(E)$ ...

ag.algebraic-geometry