This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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Non-number-theoretic class field theory?

This is a curiosity-oriented question, so references or indications are very welcomed. In the book on class field theory by Neukirch, one finds an abstract version of class-field theory: for a ...
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267 views

Problem of Scottish Book

Does anyone know if the problem 50 to Banach written in The Scottish Book is resolved? The problem is: Prove that the integral of denjoy is a Baire functional in the space M ( that is to say, in ...
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82 views

What about non finitely generated groups?

Finite groups and finitely generated groups are intensively studied, but are there interesting investigations on non finitely generated groups? I already know some references for abelian groups, so I ...
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188 views

Algorithm to calculate multiple integral.

One of the major difficulties of student in advanced calculus (including myself when student) is to obtain the extremes of repeated integrals to calculate the volume integral in $R^n$ i.e. transform ...
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80 views

Die Relationen, welche zwischen den elementaren symmetrischen Functionen bestehen - Translation?

I am trying to find a translation of this paper either in English or French (preferably English). I am not very optimistic, but i thought of asking in case somebody is more resourceful :)
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175 views

Coarse moduli space with no autmorphisms is also a fine moduli space

I'm working in the category of schemes over an algebraically closed field $k$, $Sch_k$. Suppose I have a contravariant functor $F:Sch_k\rightarrow (Set)$ which has a coarse moduli space $M$ (which is ...
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478 views

suggestion for video lectures on algebraic topology

can anyone suggest me any good video lecture series for algebraic topology other than N.J.Wildberger videos. If it is equivalent to Munkres topology (algebraic topology section) it should be great. ...
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522 views

Number of labelled graphs with $n$ nodes, $k$ edges and $t$ triangles

How many labelled undirected graphs are there with precisely $n$ vertices, $k$ edges, and $t$ triangle subgraphs? (By triangle I mean a graph with three vertices and three edges.) (Clarification: I ...
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301 views

Grothendieck on (topological) Chern Classes

I have been reading through the wikipedia article about Chern classes and it currently has a section devoted to the Alexander Grothendieck axiomatic approach. The language used throughout the section (...
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152 views

Curiosities about the content of a rare book: Topological Vector Spaces by A. Grothendieck

The book is a celebrated and highly influential book by A. Grothendeck, which was published in 1954, in French and for various reasons, it has been out of print since 1973. I am very much interested ...
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149 views

Has the $\Gamma$-like function $f_p(n) = 1^{\ln(1)^p} \cdot 2^{\ln(2)^p} \cdot \ldots \cdot n^{\ln(n)^p} $ been discussed anywhere?

In an older fiddling with the gamma-function (expanding on the idea of sums of consecutive like-powers of logarithms, similarly as the bernoulli-polynomials for the sums of like powers of consecutive ...
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176 views

Some rare binomial identities

Long ago , I once saw a nontrivial appealing binomial type of identity that I never saw again. It was something along the line of $\Sigma$$\binom{a(x)}{b(y)}$= where $a$ and $b$ where polynomials not ...
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160 views

Are there asymptotic expressions for multiple zetas $\small \zeta(s),\zeta(s,s),\zeta(s,s,s),\ldots$ where $\small s=1+\delta, \delta\to 0$?

Playing around with elementary symmetric functions I tried to generalize that to infinite series and arrived at the well known concept of MZV ("multiple zeta values"). At the moment I'm only ...
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421 views

German Analysis Texts

My question is somewhat related to this one but is somewhat more specific. Since a lot of good mathematics is written in German, I have decided to start developing my German reading abilities. So far, ...
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127 views

Direct limits of completely positive maps on $C^*$-algebras vs. operator systems

I believe I've heard, as part of the "lore," that the category (operator systems, completely positive maps) has direct limits, whereas the category ($C^*$-algebras, completely positive maps) does not. ...
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175 views

Determinant expression for the power sum

Let $S_{n,r} := \sum_{k=1}^{n} k^r$ be the power sum. On the homepage by W. Hecht (link) I have found the following determinant expression: $$S_{n,r} = (-1)^{r-1} \frac{n(n+1)}{(r+1)!} \det \begin{...
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137 views

Scale invariance and $1/f^2$ power spectrum

In the paper Occlusion Models for Natural Images : A Statistical Study of a Scale-Invariant Dead Leaves Model; Lee, A. B. Mumford, D. B. Huang, J.; International Journal of Computer Vision I read ...
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166 views

Non-closed subgroups of Lie groups

The following are my impressions from playing with a line of irrational slope $\gamma$ in the standard torus $S^1\times S^1=\mathbb{R}^2/\mathbb{Z}^2$, $\mathbb{R}\hookrightarrow \mathbb{R}\mathbb\...
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748 views

What is a linear resolution?

Can anyone tell me where I may find an introduction to linear resolutions (of a $k[x_1,\ldots,x_n]$-module or ideal) including, of course, the standard definition of such a resolution, as well as its ...
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239 views

Differential geometry text with categorial flavor

I am blown away by exposition of analytic manifolds in Serre's Lie algebras and Lie groups, I want more! Is there a text that treats classic topics of differential geometry like connections, ...
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222 views

Reference: Geometric group theory

H. Bass has studied existence of lattices on trees. Can someone suggest a (readable) reference for lattices on graphs?
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350 views

How to use Galerkin method to prove uniqueness of solutions of hyperbolic equations?

Galerkin method is used heavily in finite element method, which can conveniently convert continuous problems to discrete ones. Particularly, Galerkin method can be used to prove uniqueness existence ...
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196 views

Dual modules and first cohomology

Let $G$ be a finite group, $K$ a characteristic-$p$ algebraically closed field (say $p$ divides $|G|$), and let $M$ be a finite-dimensional $KG$-module. What hypotheses are needed on $G$, $M$ to ...
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184 views

Is there a notion of *p-adic Dedekind Domains*?

As we all know, the ring $Z_p$ can be constructed as the projective limit of the rings $Z/p^{n}Z$. Now is there any generalization such as the p-adic completions of a Dedekind Domain? This might be ...
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67 views

Reference about $\sigma$-linked posets and related notions

In this link, the following list appears: Some chain conditions [of posets], listed from easiest to satisfy to hardest to satisfy: ccc powerfully ccc productively ccc $\sigma$-...
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29 views

Weak elimination of imaginaries in the theory of the random graph

Let ${\cal U}$ be a countable random graph. Prove that for every formula $\varphi(x)\in L({\cal U})$, where $x$ has arbitrary finite arity, there are a positive integer $n$ and finite $C\subseteq{\cal ...
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69 views

Kazhdan's property (T) vs residual finiteness

There is a theorem that states that a discrete group $G$ with Kazhdan's Property $(T)$ and Property $(F)$ (so called factorisation property) is residually finite (see Kirchberg, Discrete groups with ...
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29 views

References for actions of infinite-dimensional Banach-Lie groups on infinite-dimensional Banach manifolds

I am starting to study infinite-dimensional manifolds, specifically, Banach manifolds. I found some interesting introductory texts in which the mathematical background is developed with some detail. ...
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38 views

Source request for $H^*(B\mathrm{TOP},\mathbb{Q})\cong H^*(BO,\mathbb{Q})$

Let $B\mathrm{TOP}$ denote the classifying space for microbundles, i.e. $B\operatorname{Homeo}(\mathbb{R}^n,0)$. Now we get a map from $BO$ to $B\mathrm{TOP}$ via the inclusion. Let $f$ denote the ...
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96 views

Notebooks used by Paul Erdős

Paul Erdős was known for living out of two half-full (or half-empty) suitcases; one had a few clothes and the other had mathematical papers. Some of these papers were probably referring to his ...
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46 views

Has it been proved that odd perfect numbers cannot be triangular?

(Note: This question has been cross-posted to MO.) Euclid and Euler proved that every even perfect number is of the form $m = \frac{{M_p}\left(M_p + 1\right)}{2}$ where $M_p = 2^p - 1$ is a prime ...
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41 views

Determinacy and uniformization

It's known that $PD$ implies projective uniformization. Assuming $AD$, is there an analogous theorem that holds for all subsets of the plane (where the uniformizing functions are reasonably definable ...
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52 views

Is there a dictionary for math notation?

As a non-mathematician who loves the elegance of mathematics, I'm often confused about certain syntax I see. For example, $2+2$ is "2 plus 2" obviously. But things get more complicated when, for ...
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27 views

Computing the de Rham Cohomology of $\mathbb{S}^2$ using Cech Cohomology

This might be a naïve question but I have decided to give it a try as I cannot figure out a way to give it a satisfactory answer. I've learned about de Rham's theorem relating de Rham and Cech ...
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67 views

Open problems in Lie theory

I been studying lie theory for some time. Beside classification related problems what are some examples of open problems in the lie world? Especifically in the topological/differentiable structure of ...
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59 views

Harmonic map into $S^n \times \mathbb{R}$

Consider a harmonic map $\Phi : \Sigma \to S^n \times \mathbb{R}$, where $\Sigma$ is a surface, and the metric on $S^n \times \mathbb{R}$ is given by the product metric. Choose local spherical (polar) ...
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130 views

Properties and geometrical interpretations of a specific planar vector law.

Genesis of the following thoughts. One usually define the following internal composition law on $\mathbb{R}^2$: $$+:\left\{\begin{array}{ccc} \mathbb{R}^2\times\mathbb{R}^2&\rightarrow&\...
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165 views

It is possible to get a closed-form for $\sum_{n=1}^{\infty}\frac{\sin(\frac{3\pi}{n})}{n^2}$?

I think that will not be useful to compute the Apéry's constant as $$\zeta(3)=\frac{4}{\pi}\sum_{n=1}^{\infty}\frac{1}{n^2}\int_0^{\frac{\pi}{2n}}\sin^2(3x)dx+\frac{1}{3\pi}\left(\sum_{n=1}^{\infty}\...
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0answers
81 views

Mathematics Wallpapers

I know that this sounds very silly. But I don't know where else to ask. Is there a good free site for mathematics wallpapers , pictures etc ? Most of the time it is very difficult to find exact ...
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0answers
41 views

What are some concrete examples of how Graph Theory can be applied to Finite State Machines?

Conceptually, Graph Theory is not very hard to understand, even its terminology is very intuitive, however, it appears to have a very wide range of applications, one of which is the field of Finite ...
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47 views

Signal processing and algebraic geometry

Signal processing is a pretty huge branch of what I would (maybe wrongly) call electrical engineering. I have heard here and there whispers of interesting connections between signal processing - in ...
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37 views

Homotopy fixed points of connective K-theory

Let $ku$ be the $p$-completion of the connective complex K-theory spectrum. The group $\Bbb{Z}_p^\times\cong \Delta \times \Bbb{Z}_p$ acts on $ku$, where $\Delta$ is the cyclic group of order $p-1$. ...
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72 views

Book on Algebraic Spaces?

I'm actually studying "the geometry of scheme" of Eisenbud Harris, after that I want to begin with a generalization of scheme that is algebraic spaces, I know only the book of Knutson "Algebraic ...
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108 views

Two formulae for $\pi$, probably known?

I stumbled upon (in the literature) two identities for $\pi$, but they were not referenced as they are probably well-known. Hoping someone could point out who found them first. Basically, the ...
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61 views

Original proof of Ljunngren's equation

The equation $$x^2=2y^4-1$$ was studied and solved by Ljunngren, who showed that 1,1 and 293,13 are the only integer solutions.However, his proof was very difficult and L.J.Mordell thought there must ...
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80 views

Category theory without sets

I have been reading Mac Lane's Categories for the Working Mathematician, and the prospect of developing category theory without any use of set theory is mentioned more than once in the book, but never ...
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108 views

Reference request: are levelsets/levelspaces (as defined here) used anywhere in mathematics?

Thinking about unimodal distributions in multiple dimensions, I came up with the following. Given a function $f : Y \leftarrow X$ where $X$ is a topological space, define that a levelset of $f$ is a ...
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70 views

Is the Hilbert Scheme $\operatorname{Hilb}_P(X)$ independent of the choice of ample line bundle?

The construction of the Hilbert scheme of a projective scheme $X$ requires us to fix an ample line bundle $L$ on $X$ in order to define the Hilbert polynomial $P$. Suppose that $S \subset X$ is a ...
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74 views

Best sources on complete transforms (classic orthonormal transforms) and overcomplete transforms in signal processing

In the introduction section of a thesis I read a little about classic orthonormal transforms such as Fourier, discrete cosine and wavelet transforms and their application in signal processing. Then ...