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0
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0answers
10 views

Iterated free infinite loop spaces

Let $Q$ denote $\Omega^\infty\circ \Sigma^\infty$ the free infinite loop space functor. Given some space $X$, we see that $QX$ carries all the stable homotopy information about $X$. Naturally I wanted ...
0
votes
0answers
11 views

The varieties axiomatized by join-semilattice, self-distributivity, and Fibonacci term identities

Define the Fibonacci terms $t_{n}(x,y)$ for all $n\geq 1$ by letting $t_{1}(x,y)=y,t_{2}(x,y)=x,t_{n+2}(x,y)=t_{n+1}(x,y)*t_{n}(x,y)$. For $N\geq 1$, let the variety $V_{N}$ consist of all algebras $(...
0
votes
0answers
41 views

Is this problem in $NP$?

Where is the problem 'Given two $n$ many homogeneous system of polynomials in $\mathbb Z[x_1,\dots,x_n]$ with degree $2$ do all there integer roots agree?' in the polynomial hierarchy? It is in $coNP$...
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votes
0answers
7 views

Order statistics of correlated bivariate Gaussian

Suppose $(X_1,Y_1),...,(X_n,Y_n)$ are i.i.d. bivariate Gaussian with mean zero. Each coordinate has variance 1 and correlation between coordinates is $\rho\in[-1,1]$. I'm interested in the following ...
0
votes
0answers
9 views

Adiabatic limit of the torus bundle on the circle

Let $(S^1,g_1)$ be a circle with length $L$ and $(T^2,g_2)$ a flat torus where $T^2=\mathbb C/\{\mathbb Z \oplus \mathbb Z \tau\}$ for $\text{Im}\, \tau>0$. If $(M^3,g_{\epsilon})$ has a fibration ...
0
votes
0answers
9 views

Example of a Manifold which has One Non-zero Component of Ric corresponding to Scalar Curvature

I am wondering if there is a simple example of a manifold such that, given a value for the scalar curvature $R$, I can find a manifold such that the Ricci tensor has all zero components except for one ...
0
votes
0answers
16 views

Showing a differential operator is positive semidefinite

Let $R>\lambda>\chi$ be positive real constants and $\alpha$ be a real number. The following differential operator \begin{multline} \mathcal{L}g = -\frac{d}{d\xi}\left[(1-\xi^2)\frac{dg}{d\xi}\...
1
vote
0answers
24 views

Bishop-Gromov inequality strengthened for anisotropic metrics?

The Bishop-Gromov inequality provides an upper-bound on the rate of growth of volume of a ball of radius $r$ in spaces that have a lower-bound on the Ricci curvature, $Ric \geq (n-1)K$. (I am ...
4
votes
0answers
29 views

Minimizing union of overlapping rectangles

Believe it or not, this has something to do with making triangle-free graphs bipartite... We have a collection of $k$ axis parallel rectangles with side lengths $(a_i,b_i)$. We want to arrange them (...
0
votes
1answer
27 views

Is transverse measure on a foliation without closed leaves unique?

Let $(F,\nu)$ be a Thurston's foliation on a surface $S$ with a non-zero transverse measure $\nu.$ Assume that $F$ has no closed leaves nor compact separatrices. Did anyone study such foliations? ...
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0answers
28 views

Subgroup of the symmetry group of $Zer(\zeta)$ preserving multiplicity

Let $Zer(\zeta)$ denote the multiset of the non trivial zeros of the Riemann zeta function counted with multiplicity and $G$ the group of isometries of the complex plane preserving this multiset ...
2
votes
1answer
56 views

Eigenfunctions of elliptic equations

Let $\Omega$ be a bounded region in $\mathbb{R}^n$ and $a_1, a_2$ be smooth positive functions such that $a_1-a_2$ is compactly supported in $\Omega$, and $a_i>c>0$, for some constant $c$. ...
7
votes
0answers
55 views

Symmetric function transition matrix and a non-conjecture by Stanley

Consider the transition matrix $$ p_\lambda = \sum_{\mu} R_{\lambda\mu}m_\mu $$ between the power-sum and the monomial basis. There are plenty of combinatorial descriptions of $R_{\lambda\mu}$, it is ...
5
votes
0answers
88 views

Construction of a $K(\pi,1)$-space?

My colleague suggested a proof of a fact which I have hard time to believe. Since I am not a topologist by training I am asking it here. Consider any CW-complex structure on the $d$-dimensional ...
0
votes
0answers
99 views

Why is Con(ZFC) independent from ZFC? [on hold]

I am assuming that ZFC is consistent here. By Godel's second incompleteness theorem, Con(ZFC) cannot be proved in ZFC. How do we know that it cannot be disproved? Couldn't ZFC (wrongly) claim its own ...

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