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Proof Roof

Sean Eberhard's occasional mathematical musings. Monday, 9 February 2015. A few months ago on his blog. The purpose of this post is to extend Tao's construction to the nonabelian setting. Tao already stated in his post that this should be possible, so one could say that this is just an exercise in nonabelian Fourier analysis. On the other hand the proof in the nonabelian setting more or less forces a more categorical point of view, so certain points of this exercise are instructive. By a measurable group.

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Proof Roof | seaneberhard.blogspot.com Reviews

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Sean Eberhard's occasional mathematical musings. Monday, 9 February 2015. A few months ago on his blog. The purpose of this post is to extend Tao's construction to the nonabelian setting. Tao already stated in his post that this should be possible, so one could say that this is just an exercise in nonabelian Fourier analysis. On the other hand the proof in the nonabelian setting more or less forces a more categorical point of view, so certain points of this exercise are instructive. By a measurable group.

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1 proof roof

2 group limits

3 theorem 1

4 lemma 2

5 theorem 3

6 lemma 4

7 3 quasirandomness

8 theorem 5

9 lemma 6

10 theorem 7

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Proof Roof | seaneberhard.blogspot.com Reviews

https://seaneberhard.blogspot.com

Sean Eberhard's occasional mathematical musings. Monday, 9 February 2015. A few months ago on his blog. The purpose of this post is to extend Tao's construction to the nonabelian setting. Tao already stated in his post that this should be possible, so one could say that this is just an exercise in nonabelian Fourier analysis. On the other hand the proof in the nonabelian setting more or less forces a more categorical point of view, so certain points of this exercise are instructive. By a measurable group.

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seaneberhard.blogspot.com

1

Proof Roof: February 2015

http://www.seaneberhard.blogspot.com/2015_02_01_archive.html

Sean Eberhard's occasional mathematical musings. Monday, 9 February 2015. A few months ago on his blog. The purpose of this post is to extend Tao's construction to the nonabelian setting. Tao already stated in his post that this should be possible, so one could say that this is just an exercise in nonabelian Fourier analysis. On the other hand the proof in the nonabelian setting more or less forces a more categorical point of view, so certain points of this exercise are instructive. By a measurable group.

2

Proof Roof: March 2012

http://www.seaneberhard.blogspot.com/2012_03_01_archive.html

Sean Eberhard's occasional mathematical musings. Tuesday, 27 March 2012. Before continuing, prove or disprove: If $G$ is a group, the direct power $G { times n}$ is never generated by fewer than $n$ elements. Certainly this is the case if $G$ is abelian, as in this case $G { times n}$ has a quotient of the form $ mathbf{F} p n$, i.e., an $n$-dimensional vector space over $ mathbf{F} p$. This is also the case if $n leq 2$. Examples of small size are therefore a little hard to find. Posted by Sean Eberhard.

3

Proof Roof: November 2011

http://www.seaneberhard.blogspot.com/2011_11_01_archive.html

Sean Eberhard's occasional mathematical musings. Monday, 14 November 2011. A simpler example of a nonmeasurable set. I don't claim that I'm the first person to have come up with this example; I only claim that yesterday is the first time I thought of it. This is a rather sorry state of affairs, because it's an obvious and nice example. Ldots,T {-2}(Z), T {-1}(Z), Z, T(Z), T 2(Z), ldots. ]. Since $T$ is measure-preserving, we have a contradiction as before. Posted by Sean Eberhard.

4

Proof Roof: April 2014

http://www.seaneberhard.blogspot.com/2014_04_01_archive.html

Sean Eberhard's occasional mathematical musings. Tuesday, 1 April 2014. Erdős-Turán statistical group theory. What is Erdős-Turán "statistical group theory"? Although most of their results are of the above approximate nature, they prove at least one beautiful exact counting result, and I thought I might relate it here. Theorem: If $q$ is a prime power then the proportion of $ sigma in S n$ with order not divisible by $q$ is exactly. V 1 {m 1} cdots v k {m k} : ]. M 1} cdots v k! V 1 - 1)! Where the sum r...

5

Proof Roof: October 2011

http://www.seaneberhard.blogspot.com/2011_10_01_archive.html

Sean Eberhard's occasional mathematical musings. Wednesday, 26 October 2011. A question in general topology. Recall the following theorem: Given a set $X$ with two topologies $ cal U$ and $ cal V$, with $ cal U$ weaker than $ cal V$, if $ cal U$ is Hausdorff and $ cal V$ is compact then in fact $ cal U = cal V$. In general, is there a "right" topology, in this sense? Posted by Sean Eberhard. Subscribe to: Posts (Atom). A question in general topology.

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Proof Roof

Sean Eberhard's occasional mathematical musings. Monday, 9 February 2015. A few months ago on his blog. The purpose of this post is to extend Tao's construction to the nonabelian setting. Tao already stated in his post that this should be possible, so one could say that this is just an exercise in nonabelian Fourier analysis. On the other hand the proof in the nonabelian setting more or less forces a more categorical point of view, so certain points of this exercise are instructive. By a measurable group.

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