$M$ 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 …

Is it known which Kahler manifolds are also Einstein manifolds? For example complex projective spaces are Einstein. Are the Grassmannians Einsein? Are all flag manifolds Einstein?

Hello, everyone, I want to resolve one optimal problem, with the following probability inequality constraint. $Pr(h^H(W_1 - W_2 -W_3 -U)h \geq \sigma^2) \leq \rho$ where $h \sim …

I understand that one can give a proof of each of these propositions assuming the truth of the other. But this seems a bit squishy to me, since there is a trivial sense in which a …

What invariants of a matrix determine the Smith Normal Form (SNF) of all the powers of a matrix? The question makes sense over any PID $R$. If we let $M = M_n(R)$ and $G=Gl_n(R …

A knot in S^3 is small if its complement does not contain a closed incompressible surface. Is it a generic property for knots, meaning that among all knots with less than $n$ cross …

Assume for this question that ZF set theory is sound. Now consider the language "PROVELOOP," which consists of all descriptions of Turing machines M, for which there exists a ZF p …

I just finished teaching a freshman calculus course (at an American state university), and one standard topic in the curriculum is related rates. I taught my students to answer que …

Are there any techniques for lower-bounding the angle between eigenvectors of a matrix? Or a lower bound on the related quantity of the condition number of the matrix of eigenvecto …

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?

Let $G$ be an Abelian group. Let $A \subseteq G$. In additive combinatorics, one of the primary measures of the additive structure of $A$ is its additive energy, defined as $E(A) = …

I have two finite rank free modules $M,N$ over a principal ideal domain (the ring of formal complex power series to be exact) and a homomorphism between these two modules $\phi:M\r …

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 …

Let $P,Q$ be $n$ by $n$ invertible matrices. Suppose further that $P$ and $Q$ satisfies the following equation : $$(P^{-1})^T \circ P = (Q^{-1})^T \circ Q$$ where $\circ$ denotes …

We can think of the "tangent category" of a category $\mathcal{C}$ at an object $A$ as being the abelian group objects in the overcategory $\mathcal{C}/A$ (with whatever conditions …