# Tagged Questions

This tag is used if a reference is needed in a paper or textbook on a specific result.

**4**

votes

**1**answer

187 views

### Explicit bounds for transfer results in algebraic geometry

Assume you have an ideal $I\subseteq\mathbb{Z}[X_1,\ldots,X_n]$ of the polynomial ring in $n$ variables over the integers. For any field $\Bbbk$, I can consider the ideal ...

**2**

votes

**0**answers

100 views

### Examples of Geometric Constructions in Higher Dimensions

The classical problem of geometric construction seems to be restricted to planar Euclidean Geometry with straight edge and compass as the only admissible "construction-tools".
I would like to ...

**0**

votes

**1**answer

122 views

### Hodge structure of relative cohomology groups

I need a hint or a good reference for definition of mixed Hodge structure on the relative cohomology groups ($\mathrm{H}^*(X,Y)$, $Y\subset X$ a closed subvariety of a comolex quasiprojective variety ...

**0**

votes

**0**answers

17 views

### On a tower of strongly normal extensions

Where I could see the following statement?
Let $K\subset L\subset M$ be a tower of the strongly normal extensions of differential fields. If $M$ is weakly normal over $K$, then $M$ is strongly ...

**3**

votes

**1**answer

216 views

### Was $\Sigma x$ used as quantifier?

Kurt Gödel in 1931 used $x\Pi a$ where we in contemporary notation would use $(\forall x) A$ or $(x)A$, and $Ex a$ where we would use $(\exists x) A$. I believe that I remember that $\Sigma xA$ has ...

**1**

vote

**0**answers

59 views

### Uniqueness of analytic center manifold

In a book, i have read a remark which says that the center manifold of an equilibrium point of a differential equation is not unique in general but is unique in the class of analytic manifold. The ...

**1**

vote

**0**answers

82 views

### Summing a function at integer points

For a real function $f$ defined on the reals, and real $y$, define the 2-way infinite sum
$$ F_f(y) = \sum_{i\in\mathbb Z} f(y+i). $$
If $F_f(y)$ is defined for all $y$, it is periodic of period 1.
...

**0**

votes

**0**answers

39 views

### Interpolation of Banach spaces: theta = 0, 1

Let $A_1 \subset A_0$ be Banach spaces with continuous embedding. Is $(A_0, A_1)_{i, \infty} = A_i$ for $i =0, 1$, with equivalent norms? Here, $(\cdot, \cdot)_{\theta,p}$ denotes the $K$-method of ...

**2**

votes

**0**answers

221 views

### Is this approach to the combinatorics of knots well known?

I am teaching a course on knots for the first time, and this led me to play with an approach which I have not seen in the literature. I would be surprised if no one had used it before, so I am ...

**2**

votes

**1**answer

87 views

### Boundary energy estimate of wave equations

Let $D$ be the unit disk in $\mathbb{R}^{n}$, we consider the $n$ dimension wave equation defined on $D$,
$$\square u=F$$
where $\square=\partial_{t}^{2}-\triangle$ is the standard wave operator in ...

**1**

vote

**2**answers

306 views

### Line bundles over Kähler–Hodge manifolds

A Kähler–Hodge manifold $M$ can be defined as a Kähler manifold whose Kähler form $\omega$ is integral, namely $\omega\in H^{2}(M,\mathbb{Z})$. It is known then that there always exists a Hermitian ...

**0**

votes

**0**answers

116 views

### Reference Request: Category of explicit maps between primitive recursive sets?

[Edited]
Let $\mathsf{PR}$ be the category defined as follows:
Choose a specific presentation of Primitive Recursive Arithmetic, that is, with a specific set of terms for primitive recursive ...

**0**

votes

**0**answers

29 views

### References for symmetric α-stable process (SSP) for $a>2$

Many properties of Brownian motion have been extended to SSP's for $0\leq \alpha\leq 2$ and so it is quite easy to find literature on them. However, I am currently studying the SSP for $\alpha>2$ ...

**0**

votes

**0**answers

45 views

### Reference request: Wong-Zakai smooth approximation in probabilty for stochastic differential equations

I'm looking for a result of the form: Let $B_\epsilon$ denote a "natural" smooth $\epsilon$-approximation to a $n$-dimensional Brownian motion $B$ (e.g. by mollification or simply piecewise linear) ...

**8**

votes

**0**answers

318 views

### Pairing of cohomology and homology Künneth formulas

Let $k$ be a field, and let $X$ and $Y$ be CW-complexes of finite type (although the question makes sense for $k$ a ring and for more general chain complexes of finitely generated free abelian ...

**3**

votes

**2**answers

489 views

### orbits of linear algebraic group $G({\Bbb Q}_p)$ acting on subgroups of ${\Bbb Q}_p^n$

Let $G\subseteq GL(n)$ be a linear algebraic group, and let $G({\Bbb Q}_p)\subseteq GL(V)$ act on a ${\Bbb Q}_p$-vector space V of finite dimension.
Consider the action of $G$ on abelian subgroups ...

**2**

votes

**2**answers

139 views

### Upper bounds on the edge clique cover number on special graph classes

An edge clique cover of an undirected graph $G$ is a set of cliques of $G$ such that every edge of $G$ is an edge in at least one clique in the set. The edge clique cover number $\theta(G)$ is the ...

**4**

votes

**2**answers

298 views

### Concise mathematical definition of the fusion product on the Verlinde ring?

The Verlinde ring of a (let us say) simply connected simple compact Lie group has as underlying additive group the Grothendieck group of representations of the central extension $\widehat{LG}$ of the ...

**22**

votes

**2**answers

860 views

### fake $S^{2k}\times S^{2k}$

Let $X$ be a fixed closed manifold,$S(X)$ the structure set and $Aut(X)$ the group of self homotopy equivalence of $X$.
surgery theory tells us that $\mathcal{M}(X):=S(X)/Aut(X)$ is in bijection ...

**1**

vote

**0**answers

155 views

### Property theories

Property theory is, as I have understood it, first of all characterized by an attempt to approach naive comprehension type-freely and without committing to extensionality.
There is e.g. the work of ...

**-4**

votes

**1**answer

66 views

### Resources to learn about hypergraphs [closed]

I am working on a project that is based on hyper graphs. Is there any resource that I could refer to understand the basics properties of hyper graphs ?

**1**

vote

**1**answer

78 views

### What is the fractional derivative smoothness of functions from the Zygmund class?

Let $\Lambda([0,1])$ be the Zygmund class of continuous on $[0,1]$ functions for which $$\sup h^{-1}|f(x+2h)-2f(x+h)+f(x)|<\infty.$$ What would be the exact smoothness class for the fractional ...

**1**

vote

**1**answer

74 views

### Explicit deformations of pseudo representations

Let $G$ be a group (which I will be glad to consider to be the absolute Galois group of a $p$-adic field, and so satisfies Mazur's finiteness condition which appears in his paper Deforming Galois ...

**1**

vote

**0**answers

59 views

### Quotient groups of “Abelian-times-compact”, what are they called?

In what I am doing now this class of groups appears all the way: (Hausdorff) quotient groups of $A\times K$, where $A$ are locally compact abelian groups, and $K$ compact groups.
I wonder, if this ...

**4**

votes

**3**answers

316 views

### Need examples of homotopy orbit and fixed points

I am no expert in equivariant homotopy theory. Let's say, I am planing to give a talk on homotopy fixed points and orbits. My audience will be graduate students who are doing algebraic topology or ...

**5**

votes

**1**answer

173 views

### Symmetric L-groups of integral group ring of finite cyclic groups

Where can i find the results about $L^{\ast}(\mathbb{Z}\pi)$ for $\pi$ a finite cyclic group?

**1**

vote

**0**answers

232 views

### Cubic fourfold and K3 surface: geometric constructions of Hodge isometry

Hodge structure on K3 surface (the middle line of Hodge diamond is 1 20 1) is similar to the Hodge structure of cubic fourfold (the middle line of Hodge diamond of primitive cohomology is 0 1 20 1 0). ...

**0**

votes

**0**answers

41 views

### Equivalent of Lauricella $F_D$ on an elliptic curve?

Lauricella's hypergeometric function $F_D$ is related to (weighted) configurations of points on $\mathbb{P}^1$. I am looking for generalizations to weighted point configurations on an elliptic curve. ...

**2**

votes

**1**answer

110 views

### What are some good references on the Galois theory, factorization, or minimality of differential equations?

Let $\lambda$ be a nonzero complex number and let $u(x)$ be some smooth function $\mathbb{R}\to\mathbb{C}$, not identically zero. I want to prove that if $u$ satisfies $$u'' + \lambda u'+ \lambda^2 u ...

**4**

votes

**1**answer

183 views

### Localization principle in supersymmetry

In $\S$ 9.3 of the book "Mirror symmetry" (Vafa, Zaslow eds.) the authors formulate the following general localization principle for computation of integrals with respect to both even and odd ...

**2**

votes

**0**answers

54 views

### explicit matrices for Weil ($p^2$ dimensional) representation of $Sp(4,\mathbb{F}_p)$, $p>3$

I am looking for more-or-less explicit matrices for the $p^2$ dimensional Weil representation of $Sp(4,\mathbb{F}_p)$, suitable for computer implementation. Ideally, I would like the images of the ...

**2**

votes

**1**answer

195 views

### Structure of symplectic group over finite fields

We are working over the finite field $\mathbb{F}_{q}$ of odd prime characteristic $p$ and of cardinality $q$ some power of $p$. We recall the symplectic group $Sp(4,\mathbb{F}_{q})$ as the group of ...

**10**

votes

**4**answers

471 views

### The groupoid of algebraic expressions and proofs

Fix a set of variables $V$, and suppose we're given a presentation of a monosorted algebraic theory, with variable symbols taken from $V$. For the sake of example, suppose the presentation consists of ...

**1**

vote

**0**answers

90 views

### Reference: Continuity of Eigenvectors [closed]

I am looking for an appropriate reference for the following fact. I already posted on math.stackexchange, but got no answer.
For each $X \in \mathbb{R}^{n \times n}_{\text{sym}}$ (symmetric ...

**3**

votes

**2**answers

114 views

### Positive definiteness of infinite tridiagonal matrices

I am interested in the following problem: I have an infinite symmetric tridiagonal matrix
$$
A=
\begin{bmatrix}
a_1 & b_1 & & & \\
b_1 & a_2 & b_2 & & ...

**3**

votes

**2**answers

89 views

### Accuracy of the formulas for angles between almost colinear vectors

Assume $x$ and $y$ are two vectors in $\mathbb{R}^3$ and we want to compute the acute angle $\alpha\in(0,\pi/2]$ between these two (noncolinear) vectors. There are (at least) two possibilities:
In ...

**11**

votes

**2**answers

847 views

### Banach-Zarecki theorem - who was Zarecki?

I'm writing a paper for real analysis seminar, a paper about Banach-Zarecki theorem and I need some information about the authors.
Stefan Banach - there is no problem to find information about him.
...

**7**

votes

**1**answer

177 views

### Fractal dimension of scaling limits of discrete structures

Let $S$ be the set of positive integers whose base-three expansion contains only the digits 0 and 2. The discrete set $S$ in a sense has (negative) fractal dimension $(\log 1/2)/(\log 3)$, since if ...

**1**

vote

**1**answer

174 views

### Reference request: Research done on whether the Euler prime can be the largest factor of an odd perfect number

(Note: This was cross-posted from MSE.) I posted the following reference request in MSE three (3) days ago, but was unable to elicit any responses. I am cross-posting it to MO, hoping that it is ...

**1**

vote

**1**answer

184 views

### Weisinger's thesis

I am currently reading Atkin and Li's paper on Twists of newforms and Atkin-Lehner pseudo eigenvalues and one of the references there is to Weisinger's thesis:
Weisinger J., Some results on classical ...

**1**

vote

**0**answers

85 views

### Occupancy problem with limited capacity and two types of balls [closed]

I am considering the following problem that I suspect to be standard.
One has a set of $N$ balls composed of a fraction $\alpha$ of red balls and $(1-\alpha)$ of black balls (we assume $\alpha N$ is ...

**2**

votes

**1**answer

291 views

### A result attributed to Whitney

One of the basic results of real analysis says that any closed subset of a smooth ($C^\infty$) manifold $M$ is the set of zeros of some map $\lambda\in C^\infty(M;[0,1])$. This result (or some ...

**6**

votes

**1**answer

202 views

### What is known about the boundary between Richardson's theorem and the Tarski-Seidenberg theorem?

Tarski proved that equalities and inequalities in can be decided over $\mathbb{R}[x].$ Richardson proved that adding composition with the sine and exponential functions caused the problem to become ...

**2**

votes

**2**answers

95 views

### What is the sum capacity of a scalar gaussian broadcast channel?

"On the Achievable Throughput of a Multiantenna Gaussian Broadcast Channel" by Giuseppe Carie and Shlomo Shamai talks, in part, about the following type of link (paraphrasing):
A transmitter with ...

**0**

votes

**0**answers

65 views

### Are the Standard Quantum Groups Coordinate Rings Noetherian?

Are the standard quantum groups $C_q[G]$ Noetherian and if so what is a standard reference?

**3**

votes

**0**answers

62 views

### Where does this identity involving sums of Hankel-like determinants over partitions come from?

For a partition $\lambda=( \lambda_1,\dots,\lambda_n)\vdash n$ with $\lambda_1\ge\dots\ge\lambda_n\ge0$ and any function $f:\mathbb Z\to\mathbb C$, define a Hankel-like $n\times n$ matrix ...

**3**

votes

**0**answers

83 views

### Logical framework for type theories like ML and CIC

I'm looking for a logical framework in which it is possible to easily present both intensional and extensional theories of dependent types with a partially ordered set of universes à la Russell ...

**1**

vote

**1**answer

238 views

### Pseudo-differential evolution equation

I'm looking for results (or some ideas) on the following kind of pseudo-differential evolution equation:
$$
\frac{\partial u(t,x)}{\partial t} = \int_{-\infty}^{t} B(t-s,x)\, A(x,D_{x})u(s,x)\,ds \; ...

**16**

votes

**1**answer

2k views

### Mazur secret Bourbaki report “Analyse p-adique”

Does anyone happen to know if a scan of Mazur's report exists, and, if so, where to find it? It appears in the references for Katz's "Higher congruences" and "Eisenstein measure" papers.

**12**

votes

**0**answers

246 views

### Grothendieck on polyhedra over finite fields

In Grothendieck's Sketch of a Programme he spends a few pages discussing polyhedra over arbitrary rings and concludes with some intriguing remarks on specializing polyhedra over their "most singular ...