## Top new questions this week:

### Who made the famous error in calculation that 'wasted' the final years of his life?

Sorry, I am merely a Middle School maths teacher at an Australian secondary school. I remember reading years ago about a famous mathematician (18th or 19th Century?) who calculated table upon table of …

soft-question ho.history-overview
 asked by Michael McLean 18 votes
 answered by arsmath 36 votes

### Is there a natural notion of completion of a Coxeter system?

Let $(W,S)$ be a Coxeter system. Then any element of $W$ can be written as a finite products of elements of $S$. I want some notion of a "completion" of $W$, call it $\hat{W}$, whose elements are …

gr.group-theory rt.representation-theory coxeter-groups
 asked by Sam Hopkins 15 votes
 answered by Nathan Reading 1 vote

### Silly me & Van der Waerden conjecture

So I walked into this very innocent-looking combinatorics problem, and quite soon I ended up with the problem to prove that any doubly stochastic $n \times n$ matrix has a non-zero permanent. Now …

reference-request co.combinatorics permanent
 asked by Per Alexandersson 15 votes
 answered by Anthony Quas 24 votes

### Sobolev spaces and geometry

This is a very naive question, is there a way to geometrically understand Sobolev spaces without going through analysis and PDE's? To my knowledge, Sobolev spaces where created precisely to study …

dg.differential-geometry fa.functional-analysis ap.analysis-of-pdes
 asked by Juan OS 12 votes
 answered by Piero D'Ancona 8 votes

### Why is "naive" definition of non-commutative spectrum bad?

It is well-known that the category of affine schemes is equivalent to the opposit category of commutative unital rings. So naively, one would think that the same should hold in non-commutative …

ag.algebraic-geometry noncommutative-algebra noncommutative-geometry
 asked by Sasha Patotski 12 votes
 answered by Adeel 13 votes

Without any prior exposure to the cohomology of groups, one might naively proceed by replacing a group by a sort of resolution. For instance, let's take $G = \mathbb{Z}^2$, and "resolve": $$0 \to … cohomology simplicial-stuff group-cohomology classifying-spaces crossed-modules  asked by Will 12 votes  answered by Mariano Suárez-Alvarez 3 votes ### Invariant subsets of z \mapsto z^2 Where can I find an explicit construction of closed invariant subsets of the map z \mapsto z^2 on the unit circle? Furstenberg mentions that there are continuum of such disjoint minimal sets but … ds.dynamical-systems  asked by Arkady Kitover 11 votes  answered by Anthony Quas 11 votes ## Greatest hits from previous weeks: ### Quick proofs of hard theorems Mathematics is rife with the fruit of abstraction. Many problems which first are solved via "direct" methods (long and difficult calculations, tricky estimates, and gritty technical theorems) later … big-list soft-question  asked by Paul Siegel 55 votes  answered by Paul Siegel 36 votes ### Applications of the Chinese remainder theorem As the title suggests I am interested in CRT applications. Wikipedia article on CRT lists some of the well known applications (e.g. used in the RSA algorithm, used to construct an elegant Gödel … applications examples nt.number-theory big-list  asked by JoeCamel 36 votes  answered by David Speyer 43 votes ## Can you answer these? ### Paul Erdős: Determine or estimate the number of maximal triangle-free graphs on n vertices Among the collections of the open problems of Paul Erdős on the website of Professor Fan Chung, there is one called "number of triangle-free graphs". … graph-theory  asked by Rupei Xu 4 votes ### p-adic valuation of a sum Let n_1, ..., n_k denote positive integers, and let us write$$ n_i=\prod_{j=1}^m p_j^{\alpha_{ij}} for $1\le i\le k$, where the $p_j$'s are distinct prime numbers, and $\alpha_{ij}\ge 0$ for …

nt.number-theory
 asked by Bruno 4 votes

### Classical and Quantum Chern-Simons Theory

Please excuse a sloppy question from an old user who hasn't been here in a long time. I think the expertise here is such that it can be answered anyway. Let $\Sigma$ be a two-manifold and $M$ a …

at.algebraic-topology quantum-field-theory chern-simons-theory
 asked by Minhyong Kim 8 votes
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