## Tagged Questions

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### Is there anyway to rewrite a partial differential equation using language of differential forms, tensors,.etc

My question is: usually, a partial differential equation, for example, those coming from physics, is written in a lauguage of vector calculus in a local coordinate, is there anyway …
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### Growth of Thompson’s group $F$

EDIT: Mark Sapir pointed a reference (in the comments) giving a lower bound of $2^{1/4}$ for the minimal rate. Is this the state of art? The third question remains unanswered. EN …
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### Is there a good reason why a^{2b} + b^{2a} <= 1 when a+b=1?

The following problem is not from me, yet I find it a big challenge to give a nice (in contrast to 'heavy computation') proof. The motivation for me to post it lies in its concise …
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### Group action on the real line

Hi, I was wondering about the following question: if you have a faithful action of a group G on the real line R by orientation-preserving homeomorphisms, it is easy to construct …
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### Hyperbolic pair of pants.

Suppose $Y$ is a pair of pants with a hyperbolic structure and $\gamma_i; i = 1, 2, 3$ are the geodesic boundaries of length $l_i; i=1, 2, 3$ respectively. Now consider a essential …
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### Matrix Inverse with Same Principal Minors

Given an invertible matrix $A \in \mathbb{R}^{n \times n}$, and index set $\langle n\rangle = \{ 1, \dots, n \}$, and the submatrix $A(\alpha)$ with the columns and rows of $A$ wit …
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### $f^{-1}\mathcal I \cdot \mathcal O_X$ vs $f^\ast \mathcal I$

Let $X$ ad $Y$ be (noetherian) schemes and let $\mathcal I \subseteq \mathcal O_Y$ be a sheaf of ideals on $Y$. Let $f \colon X \to Y$ be a morphism of schemes. In general the shea …
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### Sheaves on Contractible Analytic Spaces

Let $(X,\mathcal{O}_X)$ be a contractible complex analytic space. Suppose that $\mathcal{F}$ is a coherent sheaf of $\mathcal{O}_X$-modules. Can we invoke the fact that $X$ is cont …
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### can we say that $(p^2+1)/2\ne p_0^2$ where $p$ is a Mersenne prime

Let $p=2^a-1>7$ be a Mersenne prime and so $a$ is an odd prime. Can we say that $(p^2+1)/2$ is not equal to the square of a prime number? Many thanks for your help BHZ