All Questions

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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 ...
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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 $t\mapsto t_0\in \mathbb{Q}$. ...
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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 ...
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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,
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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 ...
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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 ...
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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 ...
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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 ...
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Dessins d'enfants and absolute Galois group

I would like to know what is the recent progress about the group homomorphism $$\mathrm{Gal}(\overline{\mathbf{Q}}/\mathbf{Q})\rightarrow \mathrm{Out}(\hat{F_{2}})$$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 $(x, y) = (0, -1)$?
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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
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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 $0 \leq \alpha \leq 1$, ...
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 ...
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 ...