Top new questions this week:
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I explain my title by two examples in number theory:
The rational points on elliptic curve over number fields forms a finitely generated abelian group, so its rank is an integer, but so far we do not ...
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In Section 2.3.2 of Higher Algebra, Lurie introduces the notion of generalized $\infty$-operads. This is a functor $p:\mathcal{O}^\otimes \to \mathcal{F}\mathrm{in}_\ast$ of $\infty$-categories, where ...
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In 13 Lectures on Fermat's Last Theorem, Ribenboim states the following theorem (on page 7) attributed to Cauchy:
If the first case of Fermat's theorem fails for the exponent $p$, then the sum:
$$ 1^{...
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Let $G=GL_n(\mathbb{F}_q)$, $U$, $L$, $N$ the subsets of upper-triangular unipotent, lower-triangular unipotent, all unipotent matrices respectively. Then $ULU=NU$ means that for any $g\in G$ the ...
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If we know the combinatorics of a polyhedron, and all but one of its dihedral angles, does that uniquely determine the remaining dihedral angle?
I’m happy to assume the polyhedron is simply connected, ...
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Is there software that, when the input is the shape of a drum, will produce the corresponding audible sound?
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Suppose $A$ is a commutative ring. By a "lift to the sphere" I mean a commutative ring spectrum $\mathbb{S}_A$ such that $A \simeq \mathbb{S}_A\otimes_{\mathbb{S}} \mathbb{Z}$ as commutative ...
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Greatest hits from previous weeks:
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Given the vast number of new papers / preprints that hit the internet everyday, one factor that may help papers stand out for a broader, though possibly more casual, audience is their title. This view ...
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This question is motivated by teaching : I would like to see a completely elementary proof showing for example that for all natural integers $k$ we have eventually $2^n>n^k$.
All proofs I know rely ...
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Why does mathematics seem to have a polarity bias, i.e., why are products more common than coproducts, algebras more common than coalgebras, limits more common than colimits, monads more common than ...
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I am working on my zero knowledge proofs and I am looking for a good example of a real world proof of this type. An even better answer would be a Zero Knowledge Proof that shows the statement isn't ...
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At the end of 2021, Johnny Cage asked about breakthroughs in 2021 in different mathematical disciplines. A similar question has been asked at the end of 2022, so it looks like Johnny Cage originated a ...
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I think (almost) everyone agrees that Hartshorne's Algebraic Geometry is still the best.
Then what might be the 2nd best?
It can be a book, preprint, online lecture note, webpage, etc.
One suggestion ...
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The question briefly:
Can one explain the "Dzhanibekov effect" (see youtube videos from space station or comments below) on the basis of the standard rigid body dynamics using Euler's equations? (Or ...
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Can you answer these questions?
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I encountered the following type of sum:
$$
\begin{align}
\left[
\sum_{k=1}^{t}\binom{k+i-2}{i-1}\binom{t-k+l_1-i}{l_1-i}\sum_{s=k}^{t}\binom{t-s+l_2-j+1}{l_2-j+1}\binom{s+j-3}{j-2}
\right] \tag{1} \\
...
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I have started learning about end cohomology, and as far as I understand, the zeroth end cohomology $H_e^0(M; \mathbb{Z})$ is isomorphic to the zeroth Čech cohomology $\check{H}^0(e(M); \mathbb{Z})$, ...
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Does anyone have any references on how to integrate the multivariate normal distribution over an intersection of closed half spaces?
Consider the half spaces $H \triangleq \left \{ \boldsymbol{x} : \...
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