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Some aspects of Euler's work were formalized in terms of modern infinitesimal theories by Laugwitz, McKinzie, Tuckey, and others. Referring to the latter, G. Ferraro claims that "one can see in operat …

Background Suppose $X$ is a compact metric space, and that $\varphi: X\to X$ is a homeomorphism of $X$. We say a subset $A$ of $X$ is $\varphi$-invariant if $\varphi(A) = A$. A $\varphi$-invariant s …

This is crossposted at stack exchange as https://math.stackexchange.com/questions/248391/dirac-operators-on-s1. I am trying to understand the Dirac operators associated to the 2 spinor bundles on $S^ …

There have been already several questions asking for an introduction to quantum mechanics for a mathematician, but this one is slightly different, and more restrictive. I know (some) quantum mechanic …

This question arises from an application to graphical models in probability theory, but I have abstracted that part out so only algebra remains. Let $\mathbb{R}$ denote standard field of real numbers …

I would like to understand some trivialities about log-structures. Given a log-scheme $(X,M_X)$ the log-structure $M_X$ is defined via push-out. Are there stupid examples in which this push-out is act …

Question: Given a finite simplicial complex $K$, what general techniques allow one to efficiently compute (a presentation of) the group $\text{Aut}(K)$ of $K$'s automorphisms? Since this is str …

By Hopkins Theorem it is well-known that every right (resp. left) artinian unitary ring is right (left) noetherian. Suppose that a noncommutative unitary ring R satisfies the descending chain conditio …

Let $X_{K}$ be a curve over a complete DVR $R$, $R/m:=k$ an algebraically closed field. We suppose the minimal field extension $L$ of $K$ such that $X_{L}$ has stable model $X_{R_{L}}$, and the specia …

It is well-known that the only genus one fibered knots are the trefoil and the figure-eight. On the other hand, there exist infinitely many fibered links for any fixed higher genus. My question is ab …

I want to know the source of the following "folkloric" fact about holomorphic functions. It seems well described by the phrase: The three-point characterization of holomorphy. If F is a self-m …

This is perhaps a vague question, but hopefully there exists literature on the subject. The question is motivated by an answer I gave to this question on math.SE. There exists a rather remarkable rel …

I apologize if this is something standard and/or elementary, but I was unable to find anything relevant via Google. Consider a Dirichlet series $$ f(s) = \sum_{n=1}^\infty \frac{a_n}{n^s} $$ and assu …

Is there a known elementary function bound in terms of $a,b,n$ for the $n$-th prime equal to $b$ modulo $a$ (coprime to $b$)? Bounds on Linnik's constant answer this for the first prime in each progr …

I'm having some trouble finding literature on the developing map. All the sources I could find on it seem to refer to thurston's definition in either: http://www.ucl.ac.uk/~ucahhjr/Notes/Essay.pdf or …