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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 …
Tom Copeland's user avatar
  • 10.5k
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:/ …
Keith Millar's user avatar
  • 1,252
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{ …
Peter Taylor's user avatar
  • 7,226
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 …
Amir Asghari's user avatar
  • 2,437
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 …

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