MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

Complex structure on $S^6$ gets published in Journ. Math. Phys

A paper by Gabor Etesi was published that purports to solve a major outstanding problem: Complex structure on the six dimensional sphere from a spontaneous symmetry breaking Journ. Math. Phys. 56, ...

dg.differential-geometry complex-geometry  
asked by Misha Verbitsky 45 votes

Arctangents of odd powers of the golden ratio

While trying to answer this MSE question, I found that arctangents of many odd powers of the golden ratio $\varphi=\frac{1+\sqrt5}2$ are expressible as rational linear combinations of arctangents of ...

nt.number-theory conjectures  
asked by Vladimir Reshetnikov 35 votes
answered by ARupinski 43 votes

A curious determinantal inequality

In my study, I come across the following curious inequality, which I do not know a proof yet (so I am asking it here). Let $A, B$ be $n\times n$ (Hermitian) positive definite matrices. It is very ...

linear-algebra matrices inequalities matrix-analysis  
asked by M. Lin 26 votes
answered by Terry Tao 20 votes

What is the reverse mathematical strength of the fundamental theorem of algebra?

Reverse mathematics (RM) is that area that tries to pin down exactly which axioms are necessary to prove theorems, given some weak base theory. Harvey Friedman has pointed out several times (on the ...

lo.logic reverse-math  
asked by David Roberts 25 votes
answered by Bjørn Kjos-Hanssen 20 votes

How to explain the concentration-of-measure phenomenon intuitively?

One way to phrase the "concentration-of-measure" phenomenon is that, for a Euclidean sphere $S^d$ in $d$ dimensions, for large $d$, "most of the mass is close to the equator, for any equator."1 ...

mg.metric-geometry convex-geometry intuition geometric-intuition  
asked by Joseph O'Rourke 15 votes
answered by Henry Cohn 24 votes

Number of $\mathbb F_p$ points constant mod $p$?

I have some affine varieties $X$ defined over $\mathbb Z$, and associated integers $c(X)$, with the property that $\# X_{\mathbb Z/p} \equiv c(X) \bmod p$ for all $p$. (In particular $c(X)$ is usually ...

ag.algebraic-geometry nt.number-theory diophantine-equations motives  
asked by Allen Knutson 14 votes
answered by Dan Petersen 5 votes

Does projective imply flat?

Let $\mathcal C$ be an abelian category equipped with a closed symmetric monoidal structure. This implies in particular that the monoidal structure $\otimes$ is right exact in each variable. I care ...

ct.category-theory hopf-algebras monoidal-categories flatness projective-module  
asked by Theo Johnson-Freyd 12 votes
answered by Eric Wofsey 10 votes

Greatest hits from previous weeks:

Widely accepted mathematical results that were later shown wrong?

I wonder if there are any examples in the history of mathematics of a mathematical proof that was initially reviewed and widely accepted as valid, only to be disproved a significant amount of time ...

ho.history-overview soft-question big-list  
asked by romkyns 146 votes
answered by Beren Sanders 163 votes

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

Can you answer these?

Complements of unknotted tori (higher dimensions)

It is weil-known that an unknotted 2-torus in $S^3$ provides the standard Heegaard splitting, in particular its complement consists of two solid tori. It is also known that an unknotted 3-torus in ...

gt.geometric-topology embeddings  
asked by ThiKu 4 votes

Smooth morse theory of Riemannian distance functions

Let $(M,g)$ be a Riemannian manifold, and $p\in M$. As $R>0$ increases, the topology of the ball $B(p,R)$ changes, but the changes happen only at a Lebesgue measure zero set of $R$. For instance, ...

dg.differential-geometry riemannian-geometry morse-theory  
asked by biringer 6 votes

How to get a polygon from a translation surface $(X,\omega)$

Let $S_g$ be a compact topological surface of genus $g$. I know there is the correspondence $\{$Abelian differentials on compact Riemann surfaces of genus g$\}\leftrightarrow\{$ Translation surfaces ...

at.algebraic-topology dg.differential-geometry gt.geometric-topology complex-geometry riemann-surfaces  
asked by User28341 5 votes
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