Is it true that for every integer $r$, the equation $2^m = 3^n + r$ has at most a finite number of integer solutions? I understand that this is a special case of Pillai's conjectur …

Consider a compact manifold M. For a vector field X on M, let $\phi_X$ denote the diffeomorphism of M given by the time 1 flow of X. If X and Y are two vector fields, is $\phi_X \ …

This question may end up [closed], but I'm going to ask and let the people decide. It's certainly the kind of question that I'd ask people at tea, and it's not one whose answer I' …

Hi everybody, I recently got interested in Game Theory but I don't know where should I start. Can anyone recommend any references and textbooks? And what are the prerequisites of …

The push-pull formula appears in several different incarnations. There are, at least, the following: 1) If $f \colon X \to Y$ is a continous map, then for sheaves $\mathcal{F}$ on …

Does there exist anywhere a comprehensive list of small genus modular curves $X_G$, for G a subgroup of GL(2,Z/(n))$? (say genus <= 2), together with equations? I'm particularly …

I'm sure this is standard but I don't know where to look. Let $M$ be a contractible compact smooth $n$-manifold with boundary. Does it have to be homeomorphic to $D^n$? What about …

I am studying the homotopy type of a space,and i hope it would be a $K(\pi,1)$ space. now i have find its covering,once we can say the covering is $K(\pi,1)$,so is the space itself …

Here's a question I can't answer by myself: The Reflection Principle in Set Theory states for each formula $\phi(v_{1},...,v_{n})$ and for each set M there exists a set N which ext …

Consider the 2D Shubert function. As given in that page, the function has 18 global minima and several local minima. How can I find the (x,y) of all these minima? Any help apprecia …

Let $p$ be a prime. Given a positive integer $n$, does there exist a $\beta$ in an extension of $F_p$ such that 1) If $F_p[\beta] = F_{p^N}$, then $N > n^n$; ( $\beta$ lies in a …

This question is related to this previous question. Many combinatorial configurations have Levi graphs which may be represented as derived graphs obtained from voltage graphs over …

Let $(M,g)$ be a Riemannian manifold, $p$ a point on the manifold and $v \in T_p M$. Let $\gamma$ be the geodesic starting at $p$ in the direction $v$. There exists a time $t_f$ …

Hello all, Dirichlet's famous theorem asserts that any arithmetic progression $\lbrace ax+b | x \in {\mathbb N}\rbrace$ contains infinitely many primes if a and b are relatively pr …

For every finite dimensional semi-simple Lie group $\mathfrak{g}$, we have a loop algebra $\mathfrak{g}[t,t^{-1}]$. This loop algebra has a natural invariant inner product by taki …