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I'm coming with a very basic question for which I can't find an answer. Please forgive me if I didn't search efficiently enough. What can the closure of an orbit of an element $X$ of $\mathbb{R}^2$ u …

I was wondering if anything is known about the possible structure of $\mathrm{Aut}(S)$ for a Riemann surface $S$. More precisely, are there known obstructions for a finite group $G$ to be such an auto …

I would like to find a list (or at least a description) of the maximal closed connected subgroups of $\mathrm{SL}(n, \mathbb{R})$ , and also of $\mathrm{SU}(p,q)$. In the following MO discussion is i …

I'd be interested in computing an asymptotic expansion when $h \rightarrow 0$, of an integral of the form $$ I_h = \int_{\mathbb{R}}{e^{\frac{i}{h}\varphi(x)}dx} $$ where $\varphi : \mathbb{R} \righta …

My question pertains eigenvectors of matrices with somewhat evenly distributed entries. Let $M$ be an $N \times N$ matrix with complex entries (think of $N$ as a large integer). You can assume that $M …

I am interested in the following type of problem: $M$ is a open manifold and $\mu$ an infinite measure on $M$ that is absolutely continuous with respect to the Lebesgue measure. I consider a complete …

I am looking for a reference here. Consider a two-dimensional torus $\mathrm{T}^2 =S^1 \times S^1$ together with an affine structure, that is a $(Aff(\mathbb{R}^2), \mathbb{R}^2)$-structure. Such a st …