# All Questions

**1**

vote

**1**answer

59 views

### Set of General Linear Position with Nonzero Measure

I came to the following question, but I don't have quite a good idea how to approach.
Can a set $A\subset \mathbb{R}^n , n\ge 2$ with nonzero measure be in a general linear position?
I believe ...

**1**

vote

**0**answers

57 views

### For which primes $p$ is the field $\mathbb{Q}(\Gamma(1/p^{j}))$ a strict subfield of $\mathbb{Q}(\Gamma(1/p^{i}))$ whenever $0<i<j$?

I already asked this question on a French math forum but eventually came to think that as silly it may turn out to be, perhaps something interesting could finally emerge from it, so I decided to take ...

**1**

vote

**0**answers

129 views

### Rationally connected spaces over non-algebraically-closed fields

The definition I most often see for what it means for a projective variety $X$ over a field $k$ to be rationally connected is that there exists a variety $M$ and a dominant morphism ...

**6**

votes

**1**answer

229 views

### moving up a consequence of PFA

The Proper Forcing Axiom (PFA) implies that every forcing which adds a subset of $\omega_1$ either adds a real or collapses $\omega_2$. Is it consistent that every forcing which adds a subset of ...

**19**

votes

**3**answers

2k views

### Adapting arguments and plagiarism

I'm currently working on my PhD thesis. I have several suggested problems to work on, some of them are very similar to some problems that my advisor have worked before and published already, either in ...

**14**

votes

**0**answers

308 views

+50

### Checking Mertens and the like in less than linear time or less than $\sqrt{x}$ space

Say you want to check that $|\sum_{n\leq x} \mu(n)|\leq \sqrt{x}$ for all
$x\leq X$. (I am actually interested in checking that $\sum_{n\leq x} \mu(n)/n|\leq c/\sqrt{x}$, where $c$ is a constant, and ...

**4**

votes

**1**answer

128 views

### “Identity tensor transpose” as a map $M_n \hat{\otimes} M_n \to M_n \overline{\otimes} M_n$

Equipping $M_n$ with its usual operator space structure,
$\newcommand{\ptp}{\widehat{\otimes}}$
we can form the projective tensor product of operator spaces $M_n\ptp M_n$. In particular this puts a ...

**2**

votes

**1**answer

222 views

### Local “pathologies” in spaces arising naturally in algebraic topology

I have been thinking about methods for constructing continuous paths locally in a space. These paths have domain the unit interval and map into "small" neighborhoods of points in a space. Moreover ...

**2**

votes

**0**answers

23 views

### Intuition for universal quotient maps

The universal quotient maps are precisely the descent morphisms in the category of topological spaces. In some papers of Janelidze, Tholen, Sobral, and Reiterman (see for instance Reiterman-Tholen), ...

**0**

votes

**2**answers

136 views

### Function that gives 1 only when an integer is divisible by another integer [on hold]

I need a function that takes two inputs, a and b, and returns 1 only when a is divisible by b and 0 otherwise. Can this be written in a nice mathematical way (other than using indicator functions)?

**1**

vote

**1**answer

151 views

### General Reference for surface singularities

Is there any "standard" reference for (rational) singularities on algebraic surfaces? I'm aware of Artin's papers and the one of Brieskorn (Rationale Singularitäten komplexer Flächen), but they seem ...

**6**

votes

**1**answer

844 views

### How much of modern algebraic geometry is there in modern complex(algebraic, analytic, differential) geometry?

Good day to you, people of mathoverflow. I'll get to the point. I wonder how much of modern(abstract) algebraic geometry is there in modern complex geometry?
What do I mean by complex geometry? ...

**0**

votes

**0**answers

8 views

### Does Weil-Brezin transform provide Fourier basis in C^0 on Heisenberg manifold?

I know that $L^2$ functions of the Heisenberg nilmanifold are spanned by images of the Weil-Brezin transform. Is it true that they are also dense in C^0? Is there a reference for this?

**1**

vote

**1**answer

51 views

### linear recurrence inequality of positive terms

This is a follow up on my previous linear recurrence inequality question.
I have some matrices which satisfy a linear recurrence formula of the form
$$
A_{n+1} = \alpha A_{n} + \beta A_{n-1},\qquad ...

**1**

vote

**1**answer

64 views

### $p$-adic Dirac measure as a weak limit

The standard Dirac delta is a generalised function (or measure, or distribution...) $\delta(x)$ which can be seen as a weak limit functions $\delta_n(x)$ spiked at the the origin, in the sense that:
...

**21**

votes

**3**answers

2k views

### Nelson's proof of Liouville's theorem

The paper "A proof of Liouville's theorem" by E. Nelson, published in 1961 in Proceedings of AMS, contains just one paragraph, giving a (now) standard proof that every bounded harmonic function in ...

**0**

votes

**0**answers

110 views

### A number theory question [duplicate]

Let $m,n$ be integers and $P$ be a prime and $\lambda$ be an integer such that $0 < \lambda <\sqrt p$, Can the following equation have any answer for any $m,n,p,\lambda$ except $\lambda=+-1$?
...

**2**

votes

**1**answer

63 views

### linear recurrence inequality

Given two real analytic functions, $g(x)$ and $f(x)$, on an open interval $I\subset \mathbb{R}$, it is obvious that $g(x) \leq f(x)$ does not imply $g_n \leq f_n$ (here $g_n = [x^n] g(x)$ denotes the ...

**0**

votes

**0**answers

87 views

### A number theory question related to algebraic graph theory? [on hold]

Let $m,n$ be integers and $P$ be a prime and $\lambda$ be such that $0 < \lambda <\sqrt p$, Can the following equation have any answer for any $m,n,p,\lambda$?
...

**4**

votes

**0**answers

170 views

### A suspected typo, and Deligne's image of the general fiber swallowing the special

In SGA 4.5 (Arcata V.1) Deligne writes:
Let $X$ be a complex analytic variety and $f:X\rightarrow D$ map $X$ into the
disk. Write $[0,t]$ for closed line segment with extremities 0 and $t$ in
...

**-2**

votes

**0**answers

99 views

### Non-classical real generalization of Stirling formula [on hold]

Let $x$ from $\mathbb{R}_0^+$. (Optionally $x$ can be complex , but will not be discussed.)
Be
$$F_n(x):=\frac{f(n+1)^x}{\prod\limits_{k=1}^n (1+\frac{x}{f(k)-f(0)})^{g(k)-g(k-1)}}$$
$$S_n(x):=K_f ...

**4**

votes

**1**answer

76 views

### Zeroes of global sections killed by differential operators

I asked this question some two weeks ago on StackExchange, but received no feedback of any sort ...
Let $X$ be a compact connected Riemann surface and let $\Phi:M\rightarrow N$ be an elliptic ...

**1**

vote

**1**answer

105 views

### Modified interlacing of eigenvalues

Let $A$ be a real symmetric matrix of order $n$ and $B=\begin{bmatrix}v &v &v &v\end{bmatrix}$ where $v$ is a non zero real column vector of dimension $n$. Consider $$C=\begin{bmatrix}A ...

**0**

votes

**0**answers

46 views

### Factor group lemma [closed]

I have seen the following statement in http://www.sciencedirect.com/science/article/pii/0012365X84900104 [Page 294, part 2.2], but I cannot understand why "then $\mid N\mid *[a_i: 1\leq i\leq n]$ is ...

**0**

votes

**0**answers

99 views

### Contour integral of non holomorphic but continuous functions [closed]

Let us consider two functions $f(z)$ and $g(z)$, both holomorphic on a domain $U$ (a simply connected subset of $\mathbb{C}$).
Thus, because of Cauchy's integral theorem, along any closed rectifiable ...

**2**

votes

**1**answer

170 views

### A condition for the Riemann Zeta-function by modification of its functional equation

The equation, $s\in\mathbb{C}$ with $0<\Re(s)<1$:
$$\frac{\zeta(2-s)}{\zeta(1+s)}=\frac{\Gamma(1+\frac{s}{2})}{\Gamma(1+\frac{1-s}{2})}\pi^{\frac{1}{2}-s}$$
A general question: For which ...

**7**

votes

**0**answers

134 views

+50

### Deformation of the covariant Laplacian

Let $M$ be a Riemann surface and $P \to M$ a principal $G$-bundle (with compact structure group $G$).
Fix a connection $A$ in $P$ and consider a nearby connection $B$, which is in Coulomb gauge ...

**1**

vote

**1**answer

54 views

### Counting bounded genus non-isomorphic graphs

What is the number of non-isomorphic $2n$ vertex balanced bipartite graphs of degree at most $d$ and genus $g$?
I am most interested in $d\leq3$ and $g=0$.

**3**

votes

**0**answers

47 views

### “Local” functional central limit theorem for the empirical distribution function

This question is a repost from Mathematics Stack Exchange, where it did not receive any answer.
Assume $(X_i)_{i=1}^{\infty}$ is a sequence of i.i.d. real-valued random variables such that $\mathbb ...

**3**

votes

**1**answer

170 views

### How to learn concepts of Functional Analysis which are common in PDE

I am a master student and working in PDE area. I am trying to gain deep understanding of some of the concepts in functional analysis which are common tools in PDE research, such as weak*-topology, ...

**0**

votes

**0**answers

185 views

### On the coherence of formal power series ring

Let $A = {\Bbb F}_p[[X_1,X_2,...]]$
be the ring of formal power series with infinitely many variables over the finite field ${\Bbb F}_p.$
$A$ consists of such formal sum elements as $\sum ...

**3**

votes

**1**answer

84 views

### Extension property for unipotent linear groups over rings

This is my first question, so my apologies if it is too simple/poorly motivated.
During the course of some recent research I came across a particular variant of the following problem.
Let $G$ ...

**1**

vote

**0**answers

69 views

### Convergence of an rcll process along a random subsequence

I have a process $X_s$, for $s \ge 0$, taking values in a Polish space $T$ with an rcll version where I have shown, for every nonrandom increasing sequence $s_n$, that $X_{s_n} \to c$ in probability, ...

**0**

votes

**0**answers

56 views

### Lower bound on the diameter of a ball contained in the stable manifold of a critical point

Let $f: \mathbb{R}^d \rightarrow \mathbb{R}$ be a smooth function and consider the $d$-manifold $M = \{(x, f(x)): x \in \mathbb{R}^d\} \subset \mathbb{R}^{d+1}$. Consider the negative of the gradient ...

**0**

votes

**0**answers

67 views

### “increasing” the logarithmic energy of certain measures

Let $0<a<b<1$ and $f\in L^2[0,a]$ be a real-valued function with $\int_0^af^2=1.$ Define its logarithmic energy by $$\mathcal{E}_a(f)=\int_0^a\int_0^af(x)f(y)\log\frac{1}{|x-y|}dxdy$$
Q. ...

**1**

vote

**1**answer

41 views

### Various limits of the orthogonal kernel polynomials

In a different thread, we stumbled upon the following question:
Given a continuous finite measure $w(x)dx$ on some interval $(a,b)$, $-\infty \leq a <b \leq \infty$, and the set of respective ...

**18**

votes

**1**answer

870 views

### Mathematicians with Aphantasia (Inability to Visualize Things in One's Mind)

Are there any mathematicians with aphantasia? If so, could they please elaborate upon what their experience with mathematics is like?
I realize that this question probably falls outside of the scope ...

**6**

votes

**1**answer

225 views

### “structure group” for fibration

Regarding "fibration" as a homotopy analogue of "fiber bundle",I want to see parallel notions of "structure group" and "fiber change" in "fibration".
Does it make sense to talk about "structure ...

**4**

votes

**1**answer

232 views

### Does anyone recognize this exponential sum?

For $a$, $b$ two integers, let $(a,b)$ denotes their gcd. We define the following exponential sum :
$$G_q(n):=\sum_{d|q,~(d,q/d)=1}{e^{2i\pi n\frac{dd'}{q}}}$$
for $n$ a non-negative integer and $q$ ...

**0**

votes

**0**answers

43 views

### parametrizations for sections of time in a flow

Let $\phi:\mathbb{R}\times X\rightarrow X$ be a flow in $X$, where $(X,d)$ is a compact metric space. Denote by $\mathcal{H}$ the set of continuous maps $ h:\mathbb{R}\rightarrow \mathbb{R}$ such that ...

**6**

votes

**0**answers

157 views

### Nonexistence of generic objects over $L(\mathbb{R})$

A well known result (stated and credited to Todorcevic in "Semiselective Coideals", by Farah, Mathematika, 1997, but with antecedents going back to Mathias) says that, under the appropriate large ...

**6**

votes

**0**answers

122 views

### intuitive connection between The KdV equations and the Virasoro bott group

I posted this on stack exchange but had no joy, perhaps someone here can answer : The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie ...

**4**

votes

**4**answers

207 views

### Probability theory without deductive closure

Human knowledge is not deductively closed. Uncertainty can arise from that just as much as from lack of brute facts. (When a Harvard graduate was reported to have thought that the earth is farther ...

**0**

votes

**0**answers

29 views

### Boolean Algebra - Find X [closed]

I am new to Boolean algebra. I do understand the basic rules but this is the first time I solve this kind of question. If possible, could you please prove me as many methods as possible. Thanks in ...

**1**

vote

**0**answers

74 views

### Rank diagrams of permutations $w \in S_{m}$ in the study of complete flag varieties [on hold]

I'm looking for some good references that may either prove or help to prove the following statement: Show that a matrix $r=(r_{pq})_{1 \leq p,q \leq m}$ defines a rank diagram for some pair of ...

**3**

votes

**0**answers

48 views

### Efficient CW structures on squarefree semi-algebraic set

General Setup
Given a collection of $k$ polynomials (with real coefficients) in $n$ real variables, say $f_i(x_1,\ldots,x_n)$, let $V \subset \mathbb{R}^n$ correspond to those $x$-values for which ...

**-2**

votes

**0**answers

28 views

### Weighted Average [closed]

I have 35 tons of liquid with a 21% rubber content.
I need to make a total of 75 tons with a 20% rubber content.
What percentage rubber should I add the the additional 45 tons of liquid?
And what is ...

**0**

votes

**0**answers

33 views

### What is $s$, $s\in\mathbb{N}^+$ such that $\rho(A^s)$ will be minimum? [closed]

Let $A$ be a n by n matrix and $\rho$ be the spectral radius of a matrix. What is $s$, $s\in\mathbb{N}^+$ such that $\rho(A^s)$ will be minimum?
thank you.

**9**

votes

**1**answer

273 views

### A careful roadtrip from locally symmetric spaces to algebra

I'm trying to break the classification of locally riemannian symmetric spaces to little steps to make it more comprehensible (and s.t. the technical details can be verified without drowning ...

**5**

votes

**0**answers

124 views

### Symplectic invariance of Hodge numbers?

Let $(X,\omega)$ be a compact symplectic manifold. If $J$ is a $\omega$-compatible complex structure on $X$ then $(X,\omega,J)$ is a compact Kähler manifold and so has Hodge numbers $h^{p,q}$.
My ...