# Tagged Questions

Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. In other words, questions that can be answered without making computations or applying theorems and axioms.

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### The Work of Pierre Deligne

In this biography of Pierre Deligne, there is a quote of Jacques Tits which says that "quite a few of his best ideas have never been written!". What are some of his best ideas that you have heard of ...
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### Greatly expanded new edition of a Bourbaki chapter on algebra?

Recently I discovered by accident that Bourbaki issued in 2012 a radically expanded version of their 1958 Chapter 8 Modules et anneaux semi-simples (like other chapters, initially in French) within ...
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### Name of amateur who gave a new proof of the Ramanujan-Nagell theorem?

In an article by George Johnson in the New York Times back in 1999, it says that an amateur mathematician from India once sent Ian Stewart a proof of the Ramanujan-Nagell theorem that the Diophantine ...
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### Good ways to organize old personal mathematical resources

I am wondering how the other Mathematicians organize their old mathematical resources, like calculation drafts, class and seminar notes etc. These old resources may be related to a wide range of ...
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### Origins of the Nerve Theorem

Recently, I've read two papers which have cited the Nerve Theorem, one crediting Borsuk with the result and another Leray. Here is the question: Who was the first to prove the Nerve Theorem?
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### Motivation for Hall-Witt identity

I've wondered for a while about the (Hall-)Witt identity in group theory: $[[a,b^{-1}],c]^b \cdot [[b,c^{-1}],a]^c \cdot [[c,a^{-1}]],b]^a = 1$. (Here, $x^y$ means $y^{-1}xy$ and $[x,y]$ ...
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### Research situation in the field of Information Geometry

I am now doing an article survey on the field of information geometry started by S.Amari and Barndorff-Nielson. I want to know some research situation in this field. I have read (4) and parts of (3). ...
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### “To operate the machine, it is not necessary to raise the bonnet.”

The quotation in the title is attributed to Frank Adams and appears in several places: In the preface of [2002, Operads in algebra, topology and physics]: "to operate the machine, it is not ...
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### Eilenberg's rational hiererchy of nonrational automata & languages — where is it now?

In the preface to his very influential books Automata, Languages and Machines (Volumes A, B), Samuel Eilenberg tantalizingly promised Volumes C and D dealing with "a hierarchy (called the rational ...
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### Which journals publish applied mathematics with mostly pure mathematics content?

In the spirit of Which journals publish expository work? please advise: What consistently high quality journals$^1$ today publish results that would otherwise go to a pure mathematics journal if ...
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### State of research in moduli space of flat connections

I am a recent PhD student trying to settle into a research topic. Even though I have a current project I am working on, I am not particularly enjoying it and would like to switch. Before braving the ...
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### Algebraic K-theory of a ring.

I started to learn some algebraic $K$-theory and its relation to geometric topology problems. My question is : What is the list of rings such that all their algebraic $K$-theory groups are known ? I ...
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### How much algebraic geometry do I need to study complex geometry?

As one can deduce from the questions I have asked on MO, I'm interested in complex geometry. I am aware that there are many facets to the field, some of which I am more comfortable with than others. ...
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### Use of an appendix in a long paper

I am writing a long paper (around 100 pages). I would consider 50 pages of it interesting in that it solves a problem of some significance in my field and contains an number of difficult ideas in the ...
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### Composition of two formal series

There are two formal semi-infinite Laurent series $$f_+(z)=z+\sum_{k=2}^{\infty} a_k z^k$$ and $$f_-(z)=z+\sum_{k=0}^{\infty} b_k z^{-k}$$ Their composition (we assume that this composition ...
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### triangulated/derived categories in Physics and algebraic geometry

Why do physicists care about the triangulated/derived categories? I mean what are the problems we want to approach using the machinery of triangulated/derived categories. e.g. in homological mirror ...
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### Errata in EGA, collected

There is an extensive list of EGA's errata on the books themselves, but my question is whether new errata, that is those found by various mathematicians after the publication, are collected somewhere. ...
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### Pedagogical question on Lie groups vs. matrix Lie groups

There are two common approaches taken in introductory texts on Lie groups: studying all Lie groups, or focusing only on matrix Lie groups. The main advantage of the latter approach is that one can ...
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### What would you do if you improve your own result that is submitted but not publishied?

Here is a hypothetical situation: You have proved a result and written up a paper about it. You have submitted your article to some journal and it is being reviewed. While you are waiting, you have ...
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### Etale Slice Theorem

I found the Luna's Slice Theorem very Technical. It will be helpful if someone illustrates the geometry involved in the theorem. Also why this theorem so useful? This is Luna's Slice theorem from a ...
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### Duality between large and small scale structures

A rather immediate reaction to seeing the definition of a coarse structure, at least to me, is to be reminded of a uniform structure. The axioms for a coarse structure $\mathcal{C}$ (defined by a ...
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### History of the characterization of commutative Artin rings

When it comes to the world of "classical" (pre-homological) Noetherian commutative algebra, I tend to think of most of the results (Krull's intersection theorem, the principal ideal theorem, etc.) as ...
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### Is it possible to define a perverse $t$-structure for a certain triangulated category of sheaves of spectra?

The perverse t-structure for the derived category of complexes of sheaves is certainly a mighty tool for studying cohomology. My question is: does there exist any homotopy-theoretic analogue for it (...
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### Authorship and the exact wording of a quote about mathematics

This has been troubling me for a few days now and I just can't seem to bring Google to reveal the truth. Which brings me here despite the risk of this question being closed as off-topic. A few years ...