**2**

votes

**1**answer

50 views

### Open questions on (finite) tensor categories

I would like to know about problems on (finite) tensor categories. I have read Etingof´s notes from his course at MIT. I have a question:
There exists any reference where I can find an open problem ...

**0**

votes

**0**answers

23 views

### Is it possible to cover all pairs of points at distance at most 1 by constant number of partitions into sets of diameter at most 1?

Let $n$ be a natural number and let $S_n$ be a square $[0,n] \times [0,n]$ in the plane.
We say that a partition $\mathcal{Q} = R_1 \cup \cdots \cup R_t$ of $S_n$ is simple if each of the sets $R_1, ...

**2**

votes

**0**answers

39 views

### Doubt on elementary transformations in the paper - On a family of algebraic vector bundles by Maruyama

Let $S$ be a surface. $C$ be a curve on $S$ and $i:C\hookrightarrow S$ is the inclusion. Let $E$ be a rank 2 vector bundle on $S$ and $F$ a line bundle on $C$. Suppose we have a surjection ...

**1**

vote

**1**answer

97 views

### cyclotomic polynomials with 7$^{th}$ coefficient greater than 1 in absolute value

It's known that the seventh coefficient of $\Phi_{105}(x)$ is $-2$ and that's the first occurrence of a coefficient with absolute value greater than $1$ for a cyclotomic polynomial. When I did a quick ...

**2**

votes

**1**answer

35 views

### Faithful exact functors to tensor categories

Let $P$ be a "nice" $k$-linear abelian tensor category (e.g. A tannakian category or a fusion category over a field $k$) and $F: M\to P $ an additive $k$-linear exact and faithful functor. I want to ...

**1**

vote

**0**answers

19 views

### Relationship between vertex cover and independent set for two graphs

Suppose i have a graph $G=(V,E)$ and i construct a graph $G'$ by taking each edge in $G$ and replacing it with a path containing an 'even' number of intermediate vertices. So as an example if $xy \in ...

**4**

votes

**0**answers

33 views

### Characterizing regular Galois extensions by the set of their specializations

Let $E$ and $F$ be two regular Galois extensions of $\mathbb{Q}(t)$ with group $G$, and let $E_{t_0}$ resp. $F_{t_0}$ be the residue fields corresponding to specializing $t\mapsto t_0\in \mathbb{Q}$. ...

**3**

votes

**2**answers

41 views

### Characterizing when matrices are 'dissipative'

An $n$ by $n$ matrix A is said to be dissipative with respect to a norm $\|\cdot \|$ if for all $x$ and $t\geq 0$, we have $\|e^{At}x\|\leq\|x\|$. Two matrices $A$ and $B$ are said to be jointly ...

**-5**

votes

**0**answers

25 views

### How to calculate limit problem [on hold]

can someone help me with calculating
$$ \lim_{x\to \infty} =
\left(\frac{3n^2+2n-4}{3n^2-1}\right)^n $$
Thanks,

**3**

votes

**0**answers

19 views

### Memorylessness of residence times for a Markov process

I'm stuck on the trivial problem of showing memorylessness of holding (residence) times for a continuous time homogeneous Markov chain on finite state space.
I have a homogeneous Markov process ...

**4**

votes

**0**answers

62 views

### Failure of universal flatification

Raynaud and Gruson proved a beautiful "flatification" theorem (5.2.2): If $S$ is a quasicompact, quasiseparated scheme, and $X$ is a finitely presented $S$-scheme, $M$ is an $\mathcal O_X$-module of ...

**3**

votes

**0**answers

52 views

### Anything known about elliptic integral $\frac{K'}{K}=\sqrt{2}-1$?

Is anything known about elliptic integral of the first kind when $\frac{K'}{K}=\sqrt{2}-1$, or more generally when $\frac{K'}{K}\neq\sqrt{r}$, where $r$ is rational? (Here $K=K(k)$ is elliptic ...

**0**

votes

**0**answers

19 views

### Delzant polytopes and combinatorial types

At first, let us see the following matheoverflow question,
About a Delzant polytope. (In particular dodecahedron)
The question is whether (combinatorial) regular dodecahedron can be realized as a ...

**5**

votes

**0**answers

119 views

### Dessins d'enfants and absolute Galois group

I would like to know what is the recent progress about the group homomorphism
$$ \mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})\rightarrow \mathrm{Out}(\hat{F_{2}})$$
...

**0**

votes

**1**answer

26 views

### Inverse error function in Hardy space?

Let $\mathrm{erf}(x) := \frac{2}{\sqrt{\pi}} \int_{-\infty}^x \exp(-t^2) \, dt$ be the error function $\mathrm{erf}: \mathbb{R} \to (-1,1)$. It is monotonously increasing and therefore has an inverse ...

**0**

votes

**1**answer

81 views

### separable BV space for PDE's, Whats stopping us? [on hold]

Consider the metric space BV(0,1) with the following metric
$$ d(u,v) = \|u-v\|_{L^1} + |TV(u)-TV(v)| $$. It is separable, compact, uniformly bounded and complete. So What is the really obvious thing ...

**-2**

votes

**0**answers

76 views

### direct proof for existence of antiderivative [on hold]

I wonder if anybody has tried the following kind of direct proof for the existence of an antiderivative of an analytic function on a star-shaped domain.
Theorem: Let $f:D \to \mathbb{C}$ be an ...

**5**

votes

**1**answer

38 views

### List of Bernoulli chaotic systems

Which discrete chaotic systems are known to be Bernoulli (i.e. measure theoretically isomorphic to a Bernoulli shift, one-sided or two-sided)?
I am aware that it is known for some uniformly ...

**3**

votes

**1**answer

43 views

### Can the $(n-1)$ power of the hermitian form on a compact complex $n$-fold be $\partial {\bar{\partial}}$-exact?

Let $\omega$ be the hermitian form for an hermitian metric on a compact complex manifold. Can $\omega^{n-1}$ be $\partial {\bar{\partial}}$-exact? (We know that our hermitian metric must necessarily ...

**2**

votes

**1**answer

55 views

### Intersections of translates of finite sets of integers

I am searching for a result in the literature that I am sure must be known, but I just fail to find it.
Let us starts with a simple example:
Let $A, B\subset \mathbb{Z}$ be a finite sets of integers ...

**4**

votes

**2**answers

205 views

### What does “higher monodromy” tell us about a principal bundle

Let $P \to X$ be a principal $G-$bundle and let $f: X \to BG$ be its classifying map. As I understand there's some way to associate a monodromy representation $\pi_1(X) \to G$ to it. I know how to ...

**1**

vote

**0**answers

37 views

### Can we get infinitely often better approximations for algebraic numbers from continued fractions with algebraic partial coefficients?

I am wondering how good approximations to algebraic
numbers one can get via convergents of continued fractions
with algebraic partial coefficients coefficients.
Let $\alpha$ be algebraic integer ...

**2**

votes

**1**answer

82 views

### Primitive sequence $a_i$ attaining Pillai's bound on $\sum_{i} 1/a_i$

A primitive sequence $1<a_1<\ldots<a_k\leq n$ is a sequence of integers no one of which divides any other, investigated by Erdos, Behrend and others, over the last 80 years. In fact, $\max ...

**1**

vote

**1**answer

36 views

### Is this a sufficient condition for distributivity of a lattice?

I asked this question here on Math.SE but uptil now it was not answered. So I decided to give it a try here. Thank you in advance.
If a lattice $L$ is distributive then it can be shown that for ...

**2**

votes

**0**answers

38 views

### Some questions regarding an alteration of Grzegorczyk's theory of concatenation, $\operatorname{TC}$

Consider Grzegorczyk's concatenation theory $\operatorname{TC}$, a "weak theory of words over the two letter alphabet $\Sigma=\{a,b\}$" (this from Grzegorczyk and Zdanowski's paper Undecidability and ...

**4**

votes

**0**answers

64 views

### $SL_2(\mathbb{F})$, decomposing $\mathbb{C}\{X\}$ into irreducible $G$-representations and dimensions [on hold]

Let $\mathbb{F}$ be a finite field with $q$ elements and $H = \mathbb{F}^\times$, the multiplicative group of $\mathbb{F}$. It is known that $H$ is a cyclic group of order $q - 1$, so $\widehat{H} = ...

**-3**

votes

**0**answers

32 views

### Unable to track the 8 letter word [on hold]

enter image description here
The answer would be like world XXXXXXXX
Please help me identify 8 letter word

**1**

vote

**0**answers

53 views

### completion and convergence of spectral sequence

I would like to understand the connection between $p$-adic completion and the strong convergence of a spectral sequence. Precisely, suppose $E^2_{s,t}\implies G_{s+t}$ is a first quadrant strongly ...

**9**

votes

**0**answers

237 views

### Goodwillie's notes from MSRI Lecture Series

Does anyone know where I can find an electronic version of Goodwillie's (unpublished) notes from the MSRI Lecture Series in Spring, 1990? They're mentioned/cited as such in work of Dundas-McCarthy, ...

**-3**

votes

**0**answers

22 views

### Decryption of the image attached [on hold]

enter image description here
May you please help getting the message

**2**

votes

**0**answers

21 views

### Generate harmonic polynomials for a finite group

Let $G$ be a finite group and $H_G$ be the set of harmonic polynomials. In the case of the symmetric group these polynomials are spanned by the Vandermonde determinant and all its partial derivatives. ...

**2**

votes

**0**answers

141 views

### Is Carlos Simpson's Descent available online?

I am not sure whether this question is suitable for MO. Is the paper "Descent" by Carlos Simpson in the book "Alexandre Grothendieck: A Mathematical Portrait" page 83-142 (or a similar version of that ...

**1**

vote

**1**answer

37 views

### The separated uniform space associated with $(X,\mathfrak{U})$

If $\mathfrak{U}$ is a not necessarily separated uniform structure for some set $X$, then an equivalence relation $R$ can be introduced on $X$ by letting $x R y$ provided $(x,y)\in U$ for every $U\in ...

**1**

vote

**0**answers

38 views

### A variance-preserving Boolean function

Let a random variable $X$ be given with $P_X$ supported over $\mathcal{X}$. What are the necessary conditions for the existence of a boolean function $f:\mathcal{X}\to \{0,1\}$ such that ...

**1**

vote

**1**answer

33 views

### Construction of $n$ makes $s_2(nk)<s_2(n)$

$s_2(n)$ denotes the sum of the standard base-2 digits of $n$.
For a fixed odd number $k>1$, can we construct $n\in \mathbb{Z}^+$, to make $s_2(nk)<s_2(n)$?
To clarify, that's not $s_2(nk) \lt ...

**2**

votes

**1**answer

54 views

### References about Hasse diagrams of root systems

This is to ask about references of Hasse diagrams of irreducible root systems. I found here and there nice pictures of root systems of type $E$. I would like to ask for Hasse diagrams of classical ...

**4**

votes

**0**answers

51 views

### Kernels of $SL(2,\mathbb{Z})$ representations from modular tensor categories

It is well known that if $\mathcal{C}$ is a modular tensor category then one may construct a representation of $SL(2,\mathbb{Z})$ using the $S$ and $T$ matrices of $\mathcal{C}$. This representations ...

**2**

votes

**2**answers

255 views

### Are there other integer solutions to the equation $9x^3 -1 = y^3$ besides $(x,y) =(1,2)$ and $(0, -1)$? [on hold]

Does the above Diophantine equation have other integer solutions besides $(x,y)=(1,2)$ and $(x, y) = (0, -1)$?

**13**

votes

**1**answer

902 views

### Is it possible to make an algorithm that could predict the likelihood that a program will halt?

Today I began to read about computability theory. I do not even have an elementary understanding of the topic but it certainly got me thinking. I know there is there is no 'one-for-all' algorithm that ...

**7**

votes

**1**answer

87 views

### Fundamental units with norm $-1$ in real quadratic fields

If we have distinct primes $p \equiv q \equiv 1 \pmod 4,$ with Legendre $(p|q) = (q|p) = -1,$ there is a solution to $u^2 - pq v^2 = -1$ in integers and the fundamental unit of $O_{\mathbb ...

**-1**

votes

**0**answers

31 views

### Examples of real orbits with irrational period [on hold]

Im looking for examples of periodic orbits on the real line given by piecewise analytic functions $g$.
More specific at most 2 pieces.
Im talking about integer iterations starting at $f(0)=0$ and with ...

**14**

votes

**2**answers

549 views

### What are the implications of the simple loop conjecture?

Drew Zemke recently posted a preprint on arXiv proving the Simple Loop Conjecture for 3-manifolds modeled on Sol.
Simple Loop Conjecture: Consider a 2-sided immersion $F\colon\, \Sigma\rightarrow ...

**1**

vote

**1**answer

124 views

### Problem related to Frobenius coin problem

Call a pair of integers $a,b\in\Bbb N$ with $\mathsf{gcd}(a,b)=1$ a good coprime pair if we have the property that
$$\mbox{ if }ax+by=rs\mbox{ and }ax'+by'=tu\mbox{ for some ...

**-6**

votes

**1**answer

55 views

### Simple bimodule over matrix ring [on hold]

Let given not trivial simple $R$- $R$ bimodule $M$, where $R$ - $n\times n$ matrix algebra over field $\mathbf{F}$. Is it true that $M$ is uniquely defined?

**2**

votes

**0**answers

36 views

### Positivity of semiclassical pseudodifferential operators

Let me first give some background. (My reference is Martinez's book An introduction to semiclassical and microlocal analysis)
Let $m\in\mathbb{R}$, and ...

**7**

votes

**2**answers

177 views

### Spectrum of Ring of Smooth Functions on $\mathbb{R}^n$

When we define smooth manifold, we starting with topological space $M$ which localy homeomorphic to $\mathbb{R}^n$ and setting up sheaf $\mathscr{F}(M)$ of functions on it which localy isomorphic to ...

**0**

votes

**0**answers

272 views

### Has this paper on the Tate-Shafarevich conjecture been peer-reviewed? [on hold]

It seems to be an "attempt" at serious research, but it strikes me as odd is that nobody seems to be using the result:
http://arxiv.org/abs/1309.7675

**1**

vote

**1**answer

72 views

### Regarding a new divergence function of two probability distributions

Let $X$ and $Y$ be two continuous random variables with common support and with PDF $f(x)$ and $g(y)$. For any constant $b$ with the support of $X$ and $Y$, and any constant $0 \leq \alpha \leq 1$, ...

**3**

votes

**1**answer

133 views

### Is there a description of variation of (mixed) Hodge Structures in terms of a Deligne operator?

A complex Mixed Hodge Structure is given by a complex vector space $V$ together with a descending filtration $W$ and two ascending filtrations $F,\bar{F}$ that satisfy the condition
\begin{equation}
...

**0**

votes

**0**answers

41 views

### Random process & probability problem met in wireless communication

A random process r obeys the following distribution:
$p(r,ṙ)=rb_0\exp(−\frac{r^2}{2b_0})\sqrt{2πb_2}exp(−\frac{\dot{r}^2}{2b_2})$, where $\dot{r}$ is the derivative of r in the time domain.
You can ...