I need help understanding the following condition: $u_h\in L^2(\mathbb{T}^d)$, $\|u_h\|_{L^2(\mathbb{T}^d)}=1$, where $h$ is the semiclassical parameter and $\mathbb{T}^d$ is the …

The following problem arises in the analysis of Bloom filters. Consider $m$ bins and $N=nk$ balls placed uniformly at random into the bins. A query chooses $k$ bins uniformly at …

I have some naive questions about polynomial-count affine varieties over $\mathbb{C}$: Are all reductive algebraic groups strongly polynomial-count? Are products of strongly poly …

What is the relation between $H^i_I(-)$ and $H^i_J(-)$ (cohomological functors) when $I\subset J$ are ideals of a (local) noetherian ring?

For me second-countability always felt like to be the more important and fundamental concept from general topology than separability. I wonder whether there are any points which ca …

Let $A$ and $B$ square real matrices. I know that the matrix $A+B$ has 1 as eigenvalue of multiplicity 1 and the others eigenvalues have their modulus <1. Can we say something a …

Let $T$ be the category of compactly generated weak Hausdorff spaces with model structure given by Serre fibrations, Serre cofibrations and weak homotopy equivalences. Let $G = |G. …

A Morse funnction on a smooth manifold is usually intuitively interpreted as follows: Imagine the manifold to be a mountainous landscape and the Morse function as the elevation of …

Are there tetrahedra which can be subdivided into three parts similar to the original? I believe this would require splitting one face into three parts. I know some types of tetrah …

Let $X$ be a sympletic manifold and $A\in H_2(X;\mathbb{Q})$. Let $g$ and $k$ be nonnegative integers. Assume that $$\mathcal{M}_{g,k}(X;A)$$ is dense in $$\overline{\mathcal{M}} …

Note: This question was posted in error, and should be closed as no longer relevant. The correct question is posted at http://mathoverflow.net/questions/131353/help-with-this-sys …

I define the notion of "Galois class of L functions" in the following way: $A$ is a Galois class of L functions if and only if the follwing three conditions hold simultaneously: …

In "Lectures on gauge theory and integrable systems" of M.Audin, she identifies the space of conections $\mathcal{A}$ on the trivial bundle $G\times S$ ($G$ Lie group, $S$ surface …

$M$ is a finitely generated $A$-module of dimension $d$ such that $G(M)$ is eqidimensional and $M$ does not have any embedded prime. Given $x\in I$ where $I$ is an ideal of $A$ an …

For an $n$-dimensional orientable closed manifold $M$, the simplicial volume is the infimum of the $l^1$-norm of the elements $\sum a_i \sigma_i$ ($a_i \in \mathbb{R}$) which repre …