MathOverflow Weekly Newsletter - Tuesday, July 29, 2014

Top new questions this week: 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 21 votes answered by Timothy Chow 16 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 18 votes answered by Qiaochu Yuan 21 votes function field analogy and global/absolute geometry The "function field analogy" seems to be a topic that is considerably bigger than any one existing writeup conveys. There are several old question on MO and and MathSE that ask for details. One of the … nt.number-theory complex-geometry arithmetic-geometry rigid-analytic-geometry   asked by Urs Schreiber 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 13 votes History of the connection between Riemann surfaces and complex algebraic curves As noted in the question "Links between Riemann surfaces and algebraic geometry", there are strong connections between Riemann surfaces and algebraic geometry - for example, compact Riemann surfaces … ag.algebraic-geometry complex-geometry ho.history-overview algebraic-curves riemann-surfaces   asked by Tait 13 votes answered by Leo Alonso 12 votes Not-lonely runners The lonely runner conjecture has several formulations. They all involve a number $n$ runners running on a circular track, each with a different speeds, and the conjecture is that each runner is … nt.number-theory pr.probability ds.dynamical-systems diophantine-equations   asked by Joseph O'Rourke 12 votes answered by Will Sawin 8 votes The definition of Reedy category The common definition of Reedy category seems to be this one that a Reedy category is a small category $R$ with two wide subcategories $R_+$ and $R_-$ and an ordinal-valued degree function on its … at.algebraic-topology homotopy-theory model-categories   asked by Mike Shulman 11 votes answered by Charles Rezk 5 votes Greatest hits from previous weeks: What is exceptional about the prime numbers 2 and 3? Admittedly this question is vague. But I hope to convey my point. Feel free to downvote this. Permit me to define prime number the following way: A number $n>1$ is a prime if all integers $d$ … prime-numbers   asked by P Vanchinathan 25 votes answered by Torsten Schoeneberg 29 votes Video lectures of mathematics courses available online for free It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some … ho.history-overview mathematics-education soft-question big-list   asked by alex 188 votes answered by Charles Siegel 35 votes Can you answer these? Hecke-module structure implicit in definition of automorphic forms in Borel-Jacquet's Corvallis article Let $G$ be a connected reductive group over a number field $F$, $G_\infty=\prod_{v\mid\infty} G(F_v)$, $\mathbf{A}$ the adèles of $F$, $\mathbf{A}_f$ the finite adèles of $F$. Fix a maximal compact … rt.representation-theory automorphic-forms   asked by Keenan Kidwell 8 votes Is this graph polynomial known? Can it be efficiently computed? I am a physicist, so apologies in advance for any confusing notation or terminology; I'll happily clarify. To provide a minimal amount of context, the following graph polynomial came up in my research … co.combinatorics graph-theory permutations statistical-physics   asked by Mike Hermele 9 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

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