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Feb
1
comment The Bourgain-Demeter-Guth breakthrough and the Riemann zeta function?
These are certainly interesting and relevant comments. What I think would be a great answer is the following: (1) What is the most optimistic quantitative for of VMC that one might conjecture? (2) If you plug this form of the VMC into Vinogradov-Korobov-type machinery what do you get for a zero-free region?
Jan
30
revised Decoupling in mixed norm spaces
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Jan
29
comment How small can a set system containing a large subset of every set be?
The question you pose is that of estimating Turan numbers. See, for instance: mathoverflow.net/questions/184210/….
Jan
28
comment How small can a set system containing a large subset of every set be?
@Aaron.. ah, yes! That is indeed the correct "obvious" construction. This still doesn't seem to quite match the lower bound from Fedor's answer, but it's much closer. Since posting the question, I've noted that Turan numbers are of relevance here. Perhaps using constructions related to Turan numbers (instead of all subsets of a certain size) will do even better.
Jan
28
revised How small can a set system containing a large subset of every set be?
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Jan
28
revised How small can a set system containing a large subset of every set be?
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Jan
28
comment How small can a set system containing a large subset of every set be?
Yes. I am looking for the precise form / asymptotic of the lower bound as a function of c.
Jan
28
revised How small can a set system containing a large subset of every set be?
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Jan
28
comment How small can a set system containing a large subset of every set be?
@Arturo, I'm mostly interested in the case when $1>c>0$ is fixed and $n$ is large.
Jan
28
revised How small can a set system containing a large subset of every set be?
Excluded empty set, per Arturo Magidin's comment.
Jan
28
asked How small can a set system containing a large subset of every set be?
Jan
27
answered Pointwise convergence of Fourier series, Fefferman's article
Jan
12
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Jan
11
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Dec
27
comment The Bourgain-Demeter-Guth breakthrough and the Riemann zeta function?
This is discussed by Bourgain at youtu.be/HwXA70hAEmI?t=409. It turns out that one needs the parameter k in the theorem to be a power of log N for applications to the zero free region. In this regime, the methods of both Wooley and BDG seem inferior to Vinogradov's oroginal approach (at least in their current form).
Dec
9
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Dec
9
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Dec
9
asked The Bourgain-Demeter-Guth breakthrough and the Riemann zeta function?
Nov
19
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Nov
18
accepted Where did the term “additive energy” originate?