# All Questions

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### Zeros of the derivative of Riemann's $\xi$-function

The Riemann xi function $\xi(s)$ is defined as $$\xi(s)=\frac12 s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s).$$ It is an entire function whose zeros are precisely those of $\zeta(s)$. Since $\xi$ is real ...
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### Criterion for normality of a schematic image

Consider a projective flat morphism $$f\colon X\to Y$$ between normal varieties. Let's say over the complex numbers. The geometric fibers of $f$ are all irreducible. I would like a criterion to ...
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### textbooks on modern algebraic geometry for 21st-century starters

As for learners in algebraic geometry in 21st century, is there a textbook, lecture note or anything like that to introduce algebraic geometry utilizing the language of derived categories and stacks? ...
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### Combining Pearson correlations [on hold]

I have variables a, b, c, x I know sample values A, B, C, but not X I know Pearson correlations pairwise: ax, bx, cx (and ab, ac, bc too if it helps) Now what is the most likely value for X? ...
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### Odd-cycle inequality [on hold]

Consider the stable set problem. An odd hole is a cycle with an odd number if nodes and no edges between nonadjacent nodes of the cycle. Show that if H is the node set of an odd hole, the following ...
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### Rademacher type of a Banach space is always less than or equal to 2

Before I ask my question I will provide a brief introduction. I came across the notion of Rademacher type while reading Assaf Naor's article An introduction to the Ribe program, which can be found ...
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### A surface on which all regular curves have nowhere vanishing curvature

Let $S$ be a surface in $\mathbb{R}^{3}$ such that every regular curve $\gamma\subset S$ has nowhere vanishing curvature, that is $\kappa(z)\neq 0$ for all $z\in \gamma$. Does this imply that ...
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### Groups arising as direct limits of a stationary system of primitive matrices over the integers

I am interested in the kinds of groups of the form $\displaystyle\lim_{\longrightarrow}(\mathbf{Z}^k,M)$ where $M$ is a primitive (some power of $M$ has strictly positive components) $k\times k$ ...
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### Maths to take a user chosen number to a predictable number [on hold]

As part of simple card trick, I want to allow a user to choose a number between 1 and 100 and then ask them to do various maths to lead them to the same number so their choice becomes irrelevant. One ...
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### Contractibility of a poset-indexed colimit

Let $(X,\leq)$ be a poset with distinguished element $p$, and let $P'$ be the poset of "finite chains which weakly descend to $p$" given by all $\sigma = (x_0 \geq x_1 \geq \cdots \geq x_k \geq p)$ ...
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### Reference request: Superconformal algebra

I am looking for references that deal with the basics of $\mathcal{N=1,2}$ superconformal algebras in 2D, their representations and applications to physics, in particular I want to read about spectral ...
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### Boolean algebra 1´=0 ; 0´=1 ; x+1=1 [on hold]

Hi I have a problem to solve, in Boolean algebra. I have to prove that 1´=0 ; 0´=1 ; x+1=1 I solve the first problem x*0=0 -> x*0=x*0+0=x*0+x* x´=x*(0+x´)=x*x´=0 previous 3 problems ...
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### what are the possible approximations for ideals

(Fix some local ring $(R,\mathfrak{m})$ over a field of zero characteristic.) Suppose an ideal $J$ is defined by some complicated formula/procedure. And there is no hope of computing it/or writing ...
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### Endomorphisms and almost all graphs

Is it known what fraction (almost all?) of graphs have a trivial endomorphism monoid? I can't seem to find any reference to the question. Maybe it's related to the question: what fraction of graphs ...
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### Length of Paths in Graph [on hold]

There is a very large directed graph with n number of vertices, in order of millions. We are given a number p much smaller than n, and two vertices v1 and v2. What is the efficient way of finding a ...
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### Divergence of the Lagrange interpolation on the Chebyshev nodes

Faber theorem states that for every $\lbrace x_k^{(n)} \rbrace$ there exists a continuous $f$ function such that $\| f - L_n \|_{\infty} \not\rightarrow 0$, where $L_n$ is interpolation polynomial on ...
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### Do all 0-dimensional Shimura Varieties show up (as CM points) in $\mathcal{A}_g$?

Question: Let $S$ be a 0-dimensional Shimura variety. Does $S$ necessarily admit a morphism (in the category of Shimura varieties) to $\mathcal{A}_g$ for some $g\geq 1$? Here $\mathcal{A}_g$ is the ...
51 views

### Extension of Lebesgue measure [on hold]

For $n \in \Bbb N$, can we extend the Lebesgue measure to some measure (or complete measure) on $\Bbb R^n$? Can we extend the Lebesgue measure to some measure on the power set of $\Bbb R^n$? (The ...
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### A conditional expectation question about consecutive inner products

Consider two random vectors $v=(v_1,\dots, v_n)$ and $w=(w_1,\dots, w_{n+1})$. Each $v_i \in \{-1,1\}$ independently and with equal probability. Each $w_j \in \{-1,0,1\}$ independently with equal ...
[I'd be very happy for a better question title, if anyone has any suggestions.] I have a category $C$, two functors $F,G : C \to \mbox{Cat}$, a natural transformation $\alpha : F \to G$, and a ...