This question may be a simply problem for experts. Let $G$ be a connected compact Lie group and $T$ be its maximal torus. Let $\mathfrak{g}$ and $\mathfrak{t}$ be the corresponding …

If so, can you show me how? Here's Rossmo's Formula on Wikipedia. I tried embedding images of the formula but I'm new here and that's not allowed. If you're not familiar with th …

Let $H$ be a separable infinite dimensional Hilbert space. Denote by $\mathcal{B}(H)$ the space of bounded operators on $H$, and $\mathcal{K}(H)$ the ideal of compact operators. Wh …

I'm intererested in open surjective geometric morphisms induced by fibrations of sites $S\to T$ a la Moerdijk, but as a warm-up, let's consider the case $S \to \ast$. In the case t …

My friend and I are attempting to learn about spectral sequences at the moment, and we've noticed a common theme in books about spectral sequences: no one seems to like talking abo …

My earlier related question http://mathoverflow.net/questions/134156/lower-degree-elements-in-an-algebraic-number-field has been given a clean answer for the first part. My prese …

Let C_n={0,1}^n be the hypercube and denote by G(N,p) the Erdos-Renyi random graph (edges appear independently with probability p). Assume that N=2^n. Could one pin down p=p(n) suc …

$k$ : algebraically closed field $\mathcal{C}$: category of local Artinian $k$-algebras with residue field $k$ $\hat{\mathcal{C}}$: category of complete local $k$-algebras with r …

Given $n\in\mathbb{N}$, consider the $\ell_2$ unit sphere $\mathbb{S}^{n}\subset\mathbb{R}^{n+1}$ equipped with its "geodesic" metric $\rho_n$ defined as: $\rho_n(x,y)=\arccos \Bi …

Let $R$ be a (commutative) noetherian integral domain. Let $I$ be a prime ideal of $R$. Let $S$ be a finitely generated $R$-subalgebra of $\mathrm{Frac}(R)$. Is $S \cap R_I$ nece …

Consider - for the sake of simplicity - only graphs as structures. For undirected graphs $(V, E\subseteq \binom{V}{2})$ let $E(v)$ be the set of edges $e\in E$ incident with $ …

Let's say I have a multivariate function $$ f:D \to D, D \subset \mathbb R ^n, D \text{ compact}, $$ for which there is no closed form. That is the only way to evaluate the functi …

Our team of undergraduate physicists are familiar with finding numerical approximations to the following Poisson-like PDE central to our plasma research in a torus: $\nabla^2 V = …

I'm using Samuelson's result and a chapter from Marden's monograph "The Geometry of Polynomials". These are sophisticated results. Are these independent from the Jury-Cohn test to …

Given that a 3-regular multigraph is 3-edge-colorable, is there an expression for how many 3-edge-colorings exist? (For example, if a 2-regular multigraph is 2-edge-colorable, the …