Building off of Qiaochu's comment on my answer to a previous mathoverflow question (http://mathoverflow.net/questions/130883/is-there-any-proof-that-you-feel-you-do-not-understand/ …

I was wondering which problems we get when defining toric varieties over a field of positive characteristic. For example, consider a toric map $f:(x,y)\to (x^ay^b,x^cy^d); a,b,c,d …

Let $G$ asimply connected group over $k=\bar{k}$, $B$ a Borel subgroup and $I$ the corresponding Iwahori in G(k[[t]]), $T$ a maximal torus and $K=G(k[[t]])$. Let $\lambda\in X_{*} …

I was wondering if there is a generalization of the integral discussed here to a case like, \begin{equation}\int \frac{d^dq}{q^{\nu_1}\vert \vec{q} \pm \vec{k}_1\vert ^{\nu_2}\ver …

If $T$ is a triangulated category, then the formalism of $t$-structures gives a way to find abelian subcategories inside. You're supposed to find two strictly full subcategories, …

Yeasterday I asked a question on math stackexchange which simplifies to the following: Assume that $G$ is a graded ring and $A \subseteq G$ is a homogeneous radical ideal. …

It is written in Wikipedia http://en.wikipedia.org/wiki/Groupoid, that any connected groupoid $A\rightrightarrows X$ is isomorphic to an action groupoid $G\ltimes X$ coming from a …

A partial permutation matrix $\pi$ is one with at most one 1 in any row and column (the rest 0s). Given one, we can cross out to the East and South (but not Southeast) of each 1. S …

Define a growth function to be a monotone increasing function $F: {\bf N} \to {\bf N}$, thus for instance $n \mapsto n^2$, $n \mapsto 2^n$, $n \mapsto 2^{2^n}$ are examples of grow …

The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations. Why was there the n …

Does the Fano plane mnemonic for octonion multiplication have any deeper meaning? http://upload.wikimedia.org/wikipedia/commons/2/2d/FanoPlane.svg The symmetry group of the Fano …

The action of a group $G$ on a topological space $X$ can be viewed as a functor $F: G \to \mathcal{Top}$ with $F(*)=X$. (Here I'm viewing a group as a category with one object, $ * …

I find myself unable to solve question 24.1 of T. Jech's Set Theory: If $\beta<\omega_1$ and if $2^{\aleph_{\alpha}}\leq\aleph_{\alpha+\beta}$ for a stationary set of $\ …

I need to find the maximum number of topological sorts on Direct Acyclic Graph of N-order. I've checked by running Depth first search algorithm on various Direct Acyclic graphs, an …

Let $f \in C^{\gamma}_c(\mathbb{R}) $. Let $K:\mathbb{R}^n \backslash {\vec{0}} \rightarrow \mathbb{R}^n$ be a singular integral kernel with the following properties: 1) K smooth …