bio  website  maths.ox.ac.uk/~greenbj 

location  Auckland, New Zealand  
age  38  
visits  member for  5 years 
seen  yesterday  
stats  profile views  12,441 
I'm a professor at Oxford University, on sabbatical in New Zealand until April 2014
1d

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Largest Fourier coefficient of sparse boolean function
Tom got back to me. You can indeed get such a bound by considering the (2k)th moment of f^(gamma), for which you can find a lower bound by expanding out combinatorially and using the CauchySchwarz inequality to bound the number of solutions to x_1 + ... + x_k = y_1 + ... + y_k with f(x_i), f(y_j) = 1. Then ignore the term gamma = 0 and optimise by taking k ~ n/c. 
1d

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Largest Fourier coefficient of sparse boolean function
I think Tom Sanders considered this question and may have had an argument to show that F(n,cn) > c' 2^n, where c' depends only on c, but I don't remember exactly. I'll ask him. I think this is closely related to the issue of getting a bound on the Sidon constant s(X \cup Y) in terms of s(X) and s(Y) (known, due to work of Rider in the 1970s), together with the fact that a dissociated subset of GF(2)^n is Sidon, where Sidon is in the harmonic analysis sense webpages.uidaho.edu/lnguyen/SidonSet_RieszProduct.pdf. 
Apr 23 
awarded  Yearling 
Mar 19 
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Cricket and the HardyLittlewod maximal function
From what I understand the theorem is rather trivial when applied to Bollobas's own cricketing career  run out for 0 off the second ball of his only innings. 
Jan 30 
awarded  Pundit 
Aug 26 
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Maximum sets of lattice points such that only a few points collinear
It is, in fact, a very unsolved problem to decide whether you can put $2n$ points in $[n] \times [n]$ with no three collinear, if $n$ is large. I suspect the answer is no, and that in fact one can only put $(c + o(1))n$ such points for some $c < 2$; possibly $c = 3/2$. There is a construction which achieves this. 
Apr 23 
awarded  Yearling 
Feb 18 
awarded  Enlightened 
Feb 18 
awarded  Nice Answer 
Jan 12 
awarded  Autobiographer 
Jan 12 
awarded  Disciplined 
Sep 20 
awarded  Nice Answer 
Jul 3 
awarded  Great Answer 
Jun 25 
awarded  Revival 
Jun 12 
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What are some examples of mathematicians who had an unconventional education?
The windmill in Nottingham operated by Green (no relation) can still be visited: en.wikipedia.org/wiki/Green's_Mill,_Sneinton though it is something of a detour even if one happens to be in Nottingham. Isaac Newton's home, 28 miles away, could be ticked off too for a mathematical tour of the East Midlands of England. 
Jun 10 
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Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture
I may try and read BFI. If you do it just in some critical range, rather than in the extreme generality they do with unspecified parameters $C, D, H, R, N,\dots$, my guess is it will boil down to the same basic ingredients in a different order, once one has applied a suitable decomposition into bilinear forms: Cauchy, Weyl shift, completion of sums/Fourier expansion. What else is there? 
Jun 9 
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Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture
And by the way, I think he should have called his paper "On a new bound for an incomplete Kloosterman sum to composite moduli, with applications". 
Jun 9 
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Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture
I know very little of Kloostermania, but my impression is the arguments in the BFI papers you speak of are basically the same, only the inputs are bounds for averages of Kloosterman sums over different moduli (?) coming from automorphic form theory, rather than bounds for products of Kloosterman sums to a distinct modulus. So it's just a different black box you have to believe, right? 
Jun 9 
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Philosophy behind Yitang Zhang's work on the Twin Primes Conjecture
I have to say that, now that I have studied the paper in some detail, this seems to me to be an extraordinarily accurate (if perhaps difficult to parse on a first reading) answer to the original question. 
Jun 1 
awarded  Good Answer 