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38
votes
3
answers
2k
views
Is every finite group the outer automorphism group of a finite group?
This question is essentially a reposting of this question from Math.SE, which has a partial answer. YCor suggested I repost it here.
Our starting point is a theorem of Matumoto: every group $Q$ is th …
43
votes
1
answer
4k
views
A mysterious connection between Ramanujan-type formulas for $1/\pi^k$ and hypergeometric mot...
The question below is the follow-up of this question on MathOverflow.
Motivation: As is stated in the former question, those identities(formula (35)-(44)) of $1/\pi$ attributed to Ramanujan are relate …
5
votes
Why is the Gaussian so pervasive in mathematics?
Edit 2/15/2022{
The utility of the Gaussian $e^{\frac{t^2}{2}}$--its numerous properties--derives from the nature of the coefficients of its Taylor series expansion, naturally. The coefficients, which …
10
votes
1
answer
397
views
Direct sums of operator spaces
I am interested in the $\ell^1$ analogue of direct sums for Operator spaces, e.g. Operator Space Dictionary. Briefly, and operator space is either a concrete subspace of $B(H)$, the operators on a Hi …
5
votes
Accepted
Vopenka's principle is equivalent to the existence of a strong compactness cardinal for any ...
ORIGINAL RESPONSE:
https://www.jstor.org/stable/2273786?seq=1#page_scan_tab_contents Is the article where it is from. It seems to have never been added to the library, which would be my fault.
https:/ …
17
votes
1
answer
1k
views
Why do these two Monster-related calculations yield $163$?
Fact 1: (1979, Conway and Norton)$^{1}$
"There are $194-22-9=\color{blue}{163\,}$ $\mathbb{Z}$-independent McKay-Thompson series for the Monster."
Note: There are 194 (linear) irreducible representat …
21
votes
2
answers
912
views
Define the 3d Chern-Simons TQFT on a discrete simplicial complex
Question: What is the challenge and the current status to define the 3d Chern-Simons(-Witten) (CSW) theory on a simplicial complex or on a discrete lattice? (Or is there a no-go or an obstruction behi …
18
votes
1
answer
2k
views
Uses of Zorn's Lemma when the thing is actually unique
There is a revised version, which I might substitute for this one, but I would like to keep this as evidence of priority for the "special condition".
Are there uses of the sledgehammer Zorn's Lemma th …
2
votes
1
answer
233
views
Reference: hitting time of Gaussian process
Let $X_t$ be an OU process and $Y_t$ be the Gaussian process defined by
$$
Y_t = y+\int_0^t X_s ds + W_t,
$$
for some Brownian motion independent of $X_t$. Let $y,a>0$; is there a large deviation res …
8
votes
1
answer
445
views
Can a Shelah semigroup be commutative?
A semigroup $S$ is called
$\bullet$ $n$-Shelah for a positive integer $n$ if $S=A^n$ for any subset $A\subset S$ of cardinality $|A|=|S|$;
$\bullet$ Shelah if $S$ is $n$-Shelah for some $n\in\mathbb N …
3
votes
How can I convert Meissel's/Lehmer's formula for prime counting to get sum of primes
If you consult Lehmer's paper, the terms in question arise from $$P_2(x, a) = \sum_{p_a < p_i \le \frac x{p_i}} \sum_{p_i \le p_j \le \frac x{p_i}} 1 = \sum_{p_a < p_i \le b} \left\{ \pi\left(\frac x{ …
17
votes
3
answers
3k
views
History and motivation for Tannaka, Krein, Grothendieck, Deligne et al. works on Tannaka-Kre...
I am trying to wrap my mind around Tannaka-Krein duality and it seems quite mysterious for me, as well, as its history. So let me ask:
Question: What was the motivation and historical context for wor …
4
votes
Did André Bloch or any other mathematician receive the Becquerel Prize?
I was looking for the same claim about another mathematician (namely Vazgain Avanissian) that I came to this question. Following the clues left by the previous answer and the comments, I found a menti …
7
votes
1
answer
563
views
Introduction to Finsler manifolds from the metric geometry point of view (possibly from the ...
This question is a cross post from Math.SE. I have requested the migration of the question, but unfortunately it is not possible after two months of posting. I also have found this related question, b …
5
votes
1
answer
592
views
Asymptotic behaviour of $K$-Bessel function in transition range
It is known that the famous mistake of Iwaniec-Sarnak in their paper of $L^\infty$ norm of eigenfunction of non-cocompact arithmetic surfaces in lemma (A1) is because of they did not consider the bump …