MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

Computer calculations in a paper

I think I can improve the current upper bound concerning an open problem. The ideas are purely combinatorial, but in the end I have to calculate the maximum of a really ugly, non elementary function ...

asked by Daniel Soltész 26 votes
answered by Joseph O'Rourke 15 votes

Metrics on the 3-sphere with knotted geodesics

According to answers to this question every metrics on $S^3$ admits a simple closed geodesic. Given a knot (or link) $K$, it's also quite simple to build a metric on $S^3$ such that $K$ is a geodesic ...

gt.geometric-topology riemannian-geometry knot-theory geodesics  
asked by Marco Golla 17 votes

Is there a generalization of homotopy groups to fractional dimensions

Does there exist a reasonable candidate for such an object as $\pi_{\frac12}(X)$?

at.algebraic-topology homotopy-theory  
asked by Samarkand 15 votes
answered by Dylan Wilson 14 votes

An algebraic strengthening of the Saturation Conjecture

The Saturation Conjecture (proved by Knutson-Tao) asserts that $c_{n\mu,n\nu}^{n\lambda}\neq 0\Rightarrow c_{\mu,\nu}^{\lambda} \neq 0$, where $c$ denotes a Littlewood-Richardson coefficient and $n$ ...

co.combinatorics symmetric-functions  
asked by Richard Stanley 14 votes

Minimal number of intersections in a convex $n$-gon?

For a convex polygon $P$, draw all the diagonals of $P$ and consider the intersection points made by those diagonals. Let $f(n)$ be the minimal number of such intersections where $P$ ranges over all ...

co.combinatorics discrete-geometry incidence-geometry  
asked by Dongryul Kim 14 votes

Elementary Proof of Infinitely many primes $\mathfrak{p} \in \mathbb{Z}[i]$ in the sector $\theta < \arg \mathfrak{p} <\phi $

A quick look at the primes in $\mathbb{Z}[i]$ suggests they might be evenly distributed by angle if we zoom out on a coarse enough scale. I would like ask about the much weaker statement forgetting ...

nt.number-theory prime-numbers analytic-number-theory sieve-theory  
asked by john mangual 13 votes
answered by Eric Naslund 14 votes

Intuition behind the Kodaira Vanishing Theorem?

As the question suggests, what is the intuition behind the Kodaira Vanishing Theorem? The Kodaira Vanishing Theorem says that the cohomology groups $H^q(M, L \otimes K_M)$ vanish for $q \ge 1$ when ...

ag.algebraic-geometry dg.differential-geometry complex-geometry characteristic-classes  
asked by user76356 13 votes
answered by Sándor Kovács 11 votes

Greatest hits from previous weeks:

Examples of unexpected mathematical images

I try to generate a lot of examples in my research to get a better feel for what I am doing. Sometimes, I generate a plot, or a figure, that really surprises me, and makes my research take an ...

soft-question big-list experimental-mathematics visualization  
asked by Per Alexandersson 111 votes
answered by Terry Tao 111 votes

Best Algebraic Geometry text book? (other than Hartshorne)

I think (almost) everyone agrees that Hartshorne's Algebraic Geometry is still the best. Then what might be the 2nd best? It can be a book, preprint, online lecture note, webpage, etc. One suggestion ...

ag.algebraic-geometry books big-list textbook-recommendation  
asked by sanokun 109 votes
answered by Javier Álvarez 117 votes

Can you answer these?

What does "control of a deformation problem" mean?

Is the expression "control of a deformation problem' ever defined? There are of course many examples relating a dg-Lie or L-infty algebra to a deformation problem, and the phrase is evocative. Is it ...

reference-request lie-algebras qa.quantum-algebra deformation-theory definitions  
asked by Jim Stasheff 3 votes

Characteristic Cycles and Nearby Cycles

Let $Y$ be a smooth algebraic variety over $\mathbb{C}$, let $X = Y \times \mathbb{C}$ and let $f: X \to \mathbb{C}$ be the projection. Let $M$ be a (not necessarily regular) holonomic $D_X$-module ...

d-modules perverse-sheaves  
asked by Justin Hilburn 5 votes

Which journals publish applied mathematics with mostly pure mathematics content?

In the spirit of Which journals publish expository work? please advise: What consistently high quality journals$^1$ today publish results that would otherwise go to a pure mathematics journal if ...

soft-question mp.mathematical-physics publishing applications journals  
asked by Guido Jorg 10 votes
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