Let $D$ be a divisor in a (compact) Kahler manifold $X$. Let $N$ be the total space of the normal bundle of $D$ in $X$ and identify $D$ with the zero section of $N$. Let $m\subset …

It's a standard theorem that the number of ways to write a positive integer N as the sum of two squares is given by four times the difference between its number of divisors which a …

Any recommendations for textbooks on probability and/or stochastic processes that emphasize simulation? I'll be teaching this course in the Fall.

I am wondering that what is the difference between the ways of finding unity using euclidean algo and the chinese way of finding it!????

What is the definition of a stadium curve and does it have a curvature that is defined and continuous at each of its points?

Does there exist in Euclidean 3-dimensional space R^3 a continuous 2-dimensional surface S specified by an equation of the form z-F(x,y) which satisfies the following conditions? …

Possible Duplicate: Is there a simple way to compute the number of ways to write a positive integer as the sum of three squares? Is there a nice expression for the number …

Possible Duplicate: solving f(f(x))=g(x) Here is a nice interview question for computer science people: Write a unary function f such that f(f(x)) = -x Constraints: T …

The question is similar to this one http://mathoverflow.net/questions/22523/implicit-derivative Let $x_1, x_2, x_3$ be three points in $\mathbb{R}^3$, $A=(a_{ij})$ is a $3\times 3 …

In Colmez's work on the p-adic local Langlands correspondence for ${\rm GL}_2(\mathbb{Q}_p)$, he works with ${\rm GL}_2(\mathbb{Q}_p)$-representations on $p$-adic Banach spaces whi …

Hi, everyone: I have been going over some simplicial homology recently, hoping to get some geometric insight that I don't know how to get from the algebraic machinery alone. …

Some time ago I mentioned a certain open question in an MO answer, and Pete Clark suggesting posting the question on its own. OK, so here it is: First, the setup. Let $X$ be a pr …

If X is a set and A is a subset of X containing at least two elements, then certainly for any element $a \in A$, the principal ultrafilter of $a$ contains the principal filter of A …

Just parallelling this question, that seemed not to admit an easy answer at all, let's "soft down" the category and ask the same thing in the case of $\mathcal{C}^{\infty}$-differe …

I would like to express the integral of the absolute value of a real-valued function $f$ (over a finite interval) in terms of the Fourier coefficients of $f$. Failing that, I would …