MathOverflow Weekly Newsletter
MathOverflow Weekly Newsletter

Top new questions this week:

Escape the zombie apocalypse

Consider zombies placed uniformly at random over $\mathbb{R}^2$ with asymptotic density $\mu$. You are placed at a random point and can move with speed $1$. Zombies move with speed $v\leq 1$ straight …

random-walk game-theory percolation  
asked by user1708 27 votes
answered by Anonymous 7 votes

Why do Lie algebras pop up, from a categorical point of view?

Groups pop up as automorphism groups in any category. Rings pop up as endomorphism rings in any additive category. Is there a similar way to attach a Lie algebra to an object in a category of a …

ct.category-theory lie-algebras  
asked by Matthias Künzer 22 votes
answered by Qiaochu Yuan 23 votes

Examples of famous 'workhorse' theorems

I use the term 'workhorse' to describe a theorem which is technically challenging to prove, perhaps very deep, but the statement is either uninteresting at first glance or too imposing to be …

soft-question big-list  
asked by Stanley Yao Xiao 22 votes
answered by Timothy Chow 16 votes

The lonely molecule

Suppose $n$ air molecules (infinitesimal points) are bouncing around in a unit $d$-dimensional cube, with perfectly elastic wall collisions. Let $k=n^{\frac{1}{d}}$. For example, in 3D, $d=3$, with …

nt.number-theory pr.probability mg.metric-geometry ds.dynamical-systems diophantine-equations  
asked by Joseph O'Rourke 14 votes

Is there an algorithm to write down the 27 lines of a cubic surface?

Let $S$ be a smooth cubic surface defined by $f\in \mathbb Q[x,y,z,w]$. Is there an algorithm to write down the 27 lines on $S$? Or at least find a field extension of $\mathbb Q$ over which these …

asked by B. Wellington 13 votes
answered by Joseph O'Rourke 9 votes

Why polarization of abelian varieties?

Maybe this question is not suitable for here, but I don't think I would receive a satisfactory answer in Math StackExchange. I could never understand the intuition behind polarization of abelian …

ag.algebraic-geometry abelian-varieties  
asked by user40276 13 votes
answered by Francesco Polizzi 8 votes

Fibrations and Cofibrations of spectra are "the same"

My question refers to a folklore statement that I have now seen a couple of times, but never really precise. One avatar is: "For spectra every cofibration is equivalent to a fibration" (e.g. in the …

at.algebraic-topology homotopy-theory model-categories stable-homotopy  
asked by Simon Markett 13 votes
answered by Dan Ramras 6 votes

Greatest hits from previous weeks:

What are the most misleading alternate definitions in taught mathematics?

I suppose this question can be interpreted in two ways. It is often the case that two or more equivalent (but not necessarily semantically equivalent) definitions of the same idea/object are used in …

soft-question examples teaching definitions  
asked by QPeng 56 votes
answered by Joel David Hamkins 115 votes

why study Lie algebras?

I don't mean to be rude asking this question, I know that the theory of Lie groups and Lie algebras is a very deep one, very aesthetic and that has broad applications in various areas of mathematics …

dg.differential-geometry lie-groups lie-algebras differential-equations  
asked by Olivier Bégassat 46 votes
answered by Deane Yang 67 votes

Can you answer these?

Homotopy equivalence vs weak homotopy equivalence in Gromov's h-principle

My question concerns Gromov's h-principle for open diffeomorphism-invariant partial differential relations on open manifolds; see e.g. Eliashberg/Mishachev: Introduction to the h-principle, ยง6.2.A and …

at.algebraic-topology dg.differential-geometry fa.functional-analysis sg.symplectic-geometry differential-topology  
asked by Marc Nardmann 11 votes

Can $Ded(\kappa)$ be a supremum?

Definition If there is a dense linear order w/o endpoints of size $\lambda$ with a dense subset of size $\kappa$ then write $D(\kappa,\lambda)$. $Ded(\kappa)=\sup_\lambda \{D(\kappa,\lambda)\}$. It …

lo.logic set-theory order-theory  
asked by Ioannis Souldatos 6 votes

Homogenous polynomially convex hull of $[0,1]^n$

I would like to calculate the set of $z\in \mathbb{C}^d$ such that there exists a constant $C >0$ such that for every homogeneous polynomial $p$ in $d$ variables $$|p(z)|\leq C\sup_{x\in [0,1]^d} …

asked by J. E. Pascoe 3 votes
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