MathOverflow Questions, Problems & Solutions : TransWikia.com ~ Page 16

Continuity of eigenvectors

Let $mathbb{C} ni z mapsto M(z)$ be a square matrix depending holomorphically on a parameter $z$ with the property that $operatorname{dim}ker(M(z)))=1$ for $z $ away from...

Asked on 11/16/2021

1 answer

Is there any relationship between Szemerédi's theorem and Sunflower conjecture?

I have observed some similar things between a reformulation of the Sunflower conjecture (see also conjecture 1.3 in Improved bounds for the sunflower lemma) and ...

Asked on 11/16/2021

1 answer

Commutative group stacks and Galois cohomology

"Classically", if we consider an abelian variety $A$ over some number field $k$, we get a $Gal(bar{k}/k)$-module $A(bar{k})$, or equivalently a sheaf of abelian groups on...

Asked on 11/16/2021

0 answer

Maximal order of $x^n-d$ and its dependence on $d$

It's well known that the structure of the maximal order of $mathbb{Q}[sqrt{d}]$ depends on $d$ modulo $4$: (assuming $d$ is squarefree), the maximal order is ...

Asked on 11/16/2021 by David Corwin

0 answer

Berry–Esseen bound for operator norm of matrix averages

Is there a Berry–Esseen bound for operator norm of an average of independent random matrices? Suppose $A_1, dotsc, A_n$ are independent matrices with $mathbb{E}[A_i] = I$ (the identity...

Asked on 11/14/2021

1 answer

Analyzing the decay rate of Taylor series coefficients when high-order derivatives are intractable

This could be a soft question. I am trying to show that the $n$-th Taylor series coefficient of a function is $O(n^{-5/2})$. However, because the function is a...

Asked on 11/14/2021

2 answer

Are the ordinates of the non-trivial zeros of $zeta(s)$ uniformly distributed around the mid points of Gram point intervals they can be mapped to?

Let $rho_n$ be the $n$-th non-trivial zero of $zeta(s)$ and $z_n = Im(rho_n)$ with $z_n > 0$ and $z_{n+1} ge z_n$. A well known...

Asked on 11/14/2021 by Agno

0 answer

Can a restriction of a null-homotopic spherical map be null-homopotic?

Let $n,q$ be positive integers. We are interested to the cases where $n>q$. Let $F:mathbb B^ntomathbb S^{q-1}$ be a continuous (differentiable, if needed) map, such that ...

Asked on 11/14/2021 by yaoliding

1 answer

Beginner's guide to $A_{infty}$-algebras

I have some general questions about $A_{infty}$-algebras. Altough Iunderstand bare definition from nLab I have no association how to thinkintuitively about them. Which picture...

Asked on 11/12/2021 by Ghost in Grothendieck universe

0 answer

Could Kronecker accept a proof of Goodstein's theorem?

A famous result of Goodstein asserts that the Goodstein sequence of integers terminates.For a precise statement and a short proof, see https://en.wikipedia.org/wiki/Goodstein%27s_theorem. A well known proof of...

Asked on 11/12/2021

2 answer

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