# All Questions

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### What would you want on a Lie theory cheat poster?

For some long time now I've thought about making a poster-sized "cheat sheet" with all the data about Lie groups and their representations that I occasionally need to reference. It's a moving target, ...
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### A more natural proof of Dold-Kan?

The Dold-Kan correspondence gives an equivalence of categories between $SAb$, the category of simplicial abelian groups, and $Ch_{\geq 0}$, the category of non-negatively graded chain complexes of ...
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### Is the Manickam-Miklós-Singhi Conjecture solved? [closed]

This arXiv paper is claimed to contain a proof for the MMS conjecture. But it seems that this manuscript is not yet peer reviewed by other mathematicians. I personally tried to follow the paper, but ...
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### What are the big problems in probability theory?

Most branches of mathematics have big, sexy famous open problems. Number theory has the Riemann hypothesis and the Langlands program, among many others. Geometry had the Poincaré conjecture for a long ...
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### How does one motivate the analytic continuation of the Riemann zeta function?

I saw the functional equation and its proof for the Riemann zeta function many times, but ususally the books start with, e.g. tricky change of variable of Gamma function or other seemly unmotivated ...
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### What mathematical treatment is there on the renormalization group flow in a space of Lagrangians?

What mathematical treatment is there on the renormalization group flow in a space of Lagrangians?
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### Between mu- and primitive recursion

It is well known that primitive recursion is not powerful enough to express all functions, Ackermann function being probably the best known example. Now, in the logic courses (that I have had look ...
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### Can eta invariant be written in terms of topological data?

The eta invariant was introduced by Atiyah, Patodi, and Singer. It roughly measures the asymmetry of the spectrum of a self-adjoint elliptic operator with respect to the origin. In the paper "Exotic ...
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### Polynomial bijection from $\mathbb Q\times\mathbb Q$ to $\mathbb Q$?

Is there any polynomial $f(x,y)\in{\mathbb Q}[x,y]{}\$ such that $f:\mathbb{Q}\times\mathbb{Q} \rightarrow\mathbb{Q}$ is a bijection?
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### Occasional'' Laurent phenomenon

This question is motivated by Richard Stanley's A question on the Laurent phenomenon (motivated by his answer to the question what is the probability that a scissor became the champion?). He asked ...
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### Inconsistent theory with long contradiction

What can one say about an inconsistent theory $T$ which has no contradictions (i.e. deductions of $P \wedge \neg P$) of length shorter than $n$, where $n$ is some huge number? There have been some ...
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### Existence of parametrizations of rational orthogonal matrices

I suppose that there are formulas which parametrize all the orthogonal matrices with rational coefficients. Does anyone know anything about it? And what are some publications that discuss this? ...
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### Status of PL topology

I posted this question on math stackexchange but received no answers. Since I know there are more people knowledgeable in geometric and piecewise-linear (PL) topology here, I'm reposting the question. ...
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### nonstandard analysis book recommendation

I wish to learn nonstandard analysis. Are there any good book recommendations? I'm familiar with the ZFC system, and learnt analysis the classical way. I've found some undergraduate texts, but they ...
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### Why are fusion categories interesting?

In the same vein as Kate and Scott's questions, why are fusion categories interesting? I know that given a "suitably nice" fusion category (which probably means adding adjectives such as "unitary," ...
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### Groups that do not exist

In the long process that resulted in the classification of finite simple groups, some of the exceptional groups were only shown to exist after people had computed (most of) their character tables and ...
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### Atiyah-Singer index theorem

Every year or so I make an attempt to "really" learn the Atiyah-Singer index theorem. I always find that I give up because my analysis background is too weak -- most of the sources spend a lot of ...
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### Construction of the Stiefel-Whitney and Chern Classes

I've seen two constructions of these characteristic classes. The first comes from Milnor and Stasheff's book and involves the Thom isomorphism and (at least for me) the rather mysterious Steenrod ...
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### Flatness and local freeness

The following statement is well-known: $A$ a commutative Noetherian ring, $M$ a finitely generated $A$-module. Than $M$ is flat if and only if $M_{\mathfrak{p}}$ is free for all $\mathfrak{p}$. My ...
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### Finite extension of fields with no primitive element

What is an example of a finite field extension which is not generated by a single element? Background: A finite field extension E of F is generated by a primitive element if and only if there are a ...
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### How would you solve this tantalizing Halmos problem?

1-ab invertible => 1-ba invertible has a slick power series "proof" as below, where Halmos asks for an explanation of why this tantalizing derivation succeeds. Do you know one? Geometric series. In ...
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### Teaching a pedagogy course

At my institution incoming graduate students must take a semester long course on pedagogy taught by current grad students. I may soon be in the position of having to teach this course and I'm looking ...
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### Toy Models of Quantum Mechanics

Do toy models of quantum mechanics help us better understand "regular" quantum mechanics? For example, if we look at quantum mechanics over a finite field $F$ (e.g. $\mathbb{Z}_2$), can this lead to ...
If M is a sufficiently nice model category and D is a small category then there are two natural model structures we can impose on the functor category $Fun(D,M)$ where the weak equivalences are the ...