Questions tagged [big-list]
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
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What are some open problems in geometric probability?
What are some open problems in geometric probability?
Context: My question, "A tetrahedron's vertices are random points on a sphere. What is the probability that the tetrahedron's four faces are ...
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List of crowdsourced math projects actively seeking participants
I believe that with the advent of modern online collaboration platforms (such as Github), proof assistant languages (such as Lean), and (potentially) AI tools, there are many emerging opportunities ...
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When does the choice of the fundamental sequence matter?
I am quoting a paragraph from the second paper of Jockush and Shore on REA operators about generating the REA sets recursively via a system of notations:
"We can then associate $R$-sets with this ...
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(A list of ) Poisson structures on contact manifold
In this question I search for a list of Poisson structures defined on a contact manifold.
Recall that a Poisson structure on a manifold $M$ is a Lie algebra bracket $\{.,.\}$ on $C^\...
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Spectral sequences every mathematician should know
Reading mathematical articles, I sometimes see how mathematicians pull out amazing spectral sequences seemingly at will. While many are built using standard techniques like exact couples or filtered ...
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Which pairs of mutually contradicting conjectures are there?
Years ago I had the pleasure of witnessing Simon Thomas giving a wonderful talk about Martin's conjecture, which I just now fondly remembered reading this question. Even though I am not well-versed in ...
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Graphical software tools for quick and easy diagrams
What tools do people use for quickly and easily creating presentable, if not publication quality, diagrams of various kinds?
When I need to make a high quality diagram, I'm happy to whip up some TikZ. ...
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Improving readability of proofs
What do you do to improve the readability of finished proofs?
I basically found out that I keep a small mental checklist of criteria that I always go through after a proof is finished to improve the ...
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How do the number-theoretic properties of $n$ manifest in the algebraic/topological structure of $\Bbb R^n$?
$\DeclareMathOperator{\SO}{\mathsf{SO}}$It is well-known that certain low-dimensional Euclidean spaces have "special" properties that do not generalize. For example:
$\Bbb R^2$ is naturally ...
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How might mathematics have been different?
I think most people believe that mathematical truths are logically necessary. The fact that $\sqrt{2}$ is irrational doesn't depend on who proved it, when they proved it, whether they liked it, or ...
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Naming categories beyond their objects
Can you provide a known instance where it becomes necessary or useful to introduce a different name for the objects of a category and for the category itself?
Specifically, I am interested in cases ...
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Applications of analysis in homotopy theory and vice-versa
Working up to homotopy looks, on a surface level, incompatible with the usual properties studied in analysis, since one can e.g. homotopy deform a $C^\infty$ function into one that isn't ...
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Collect characterizations of amenability of group as many as possible
My hobby is to collect characterizations of amenability of group as many as possible. If the accumulation amounts to 365, then I'm planning to make a day-by-day calendar which deals with one of them ...
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What theorems or insights are well known for $\infty$-categories but not well known for categories?
Many theorems in $1$- and $2$-category theory have direct analogues in $(\infty, 1)$- and $(\infty, 2)$-category theory. By "direct analogue", I mean a valid statement in category theory ...
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Computer algebra systems implementing Schubert polynomials
I've had a python package out for multiplying Schubert polynomials, double Schubert polynomial, quantum Schubert polynomials, and double quantum Schubert polynomials for a little over a year. Recently ...
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