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## Tagged Questions

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### Where did Sophus Lie write the group commutator for two one parameter groups.

If $X,Y$ are vector fields and $\def\Fl{\operatorname{Fl}}\Fl^X_t$ and $\Fl^Y_t$ their local flows, let $[\Fl^X_t,\Fl^Y_t]:= \Fl^Y_{-t}\Fl^X_{-t}\Fl^Y_t\Fl^X_t$ denote the group co …
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### Local boundary symmetrisation of Riemannian metrics by coordinate changes

Assume we have a smooth Riemannian metric $g$ on a small one-sided neighborhood $U$ of $0$ on the plane, say $U_\epsilon=\lbrace(x, y): x^2+y^2<\epsilon, y\geq 0\rbrace$. When …
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### Why is there no stack of $\ell$-adic sheaves on a curve?

One of the main players in the categorical geometric langlands correspondence is the moduli stack of rank n integrable connections on a complex curve. The reason for considering s …
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### Numerical multivariate definite integration

I need to compute a set of multivariate definite integrals with infinite integration domain \displaystyle \int_{-\infty}^{\infty} \cdots \int_{-\infty}^{\infty} f(x_1,x_2, \ldo …
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### totally disconnected and zero-dimensional spaces

When do the notions of totally disconnected space and zero-dimensional space coincide? From what I gather, there are at least three common notions of topological dimension: coverin …
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### Construction of an integral point set given the set of distances ,its minimal description so as to get a measure of its complexity and its unique identifier.

Given a set of distances between every pair of points of an integral point set P of n points; say D = {${d_i}$} Q1. What is the least time complexity possible/known for …
Let me begin with an example. Consider the computable function $f(x) = 2x$. A Turing machine can implement this function in $O(|n|)$ steps: simply walk to the end of the input st …
Let $R$ be a (commutative) noetherian integral domain. Let $I$ be a prime ideal of $R$. Let $S$ be a finitely generated $R$-subalgebra of $\mathrm{Frac}(R)$. Is $S \cap R_I$ nece …