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New bounds for Szemeredi’s theorem, Ia: Progressions of length 4 in finite field geometries revisited
Ben Green and I have just uploaded to the arXiv our paper “New bounds for Szemeredi’s theorem, Ia: Progressions of length 4 in finite field geometries revisited“, submitted to Proc. … more →
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New bounds for Szemeredi's theorem, Ia: Progressions of length 4 in finite field geometries revisited
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wrote 2 weeks ago: Ben Green and I have just uploaded to the arXiv our paper “New bounds for Szemeredi’s th … more →
Some ingredients in Szemerédi's proof of Szemerédi's theorem
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wrote 2 months ago: A few days ago, Endre Szemerédi was awarded the 2012 Abel prize “for his fundamental co … more →
254A, addendum: Some notes on nilprogressions
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wrote 2 months ago: This is an addendum to last quarter’s course notes on Hilbert’s fifth problem, which I a … more →
254B, Notes 7: Sieving and expanders
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wrote 2 months ago: In this final set of course notes, we discuss how (a generalisation of) the expansion results obtain … more →
254B, Notes 5: Product theorems, pivot arguments, and the Larsen-Pink non-concentration inequality
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wrote 3 months ago: In the previous set of notes, we saw that one could derive expansion of Cayley graphs from three ing … more →
Point.Blank, Siberun, Popeska, MATHCO, Helicopter Showdown & Sluggo
wrote 3 months ago: As you can tell by the mouthful of a title this post has a lot of awesome tracks! First up I got an … more →
254B, Notes 4: The Bourgain-Gamburd expansion machine
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wrote 4 months ago: We have now seen two ways to construct expander Cayley graphs . The first, discussed in Notes 2, is … more →
Continued fractions, Bohr sets, and the Littlewood conjecture
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wrote 4 months ago: Let be an element of the unit circle, let , and let . We define the (rank one) Bohr set to be the se … more →
A variant of Kemperman's theorem
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wrote 5 months ago: In 1964, Kemperman established the following result: Theorem 1 Let be a compact connected group, wit … more →
A nilpotent Freiman dimension lemma
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wrote 5 months ago: Emmanuel Breuillard, Ben Green and I have just uploaded to the arXiv the short paper “A nilpot … more →
254B, Notes 1: Basic theory of expander graphs
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wrote 5 months ago: The objective of this course is to present a number of recent constructions of expander graphs, whic … more →
The number of cycles in a random permutation
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wrote 6 months ago: Let be a natural number, and let be a permutation of , drawn uniformly at random. Using the cycle de … more →
Some notes on the Coven-Meyerowitz conjecture
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wrote 6 months ago: Let be a finite additive group. A tiling pair is a pair of non-empty subsets such that every element … more →
254A, Notes 8: The microstructure of approximate groups
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wrote 6 months ago: A common theme in mathematical analysis (particularly in analysis of a “geometric” or … more →
The structure of approximate groups
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wrote 7 months ago: Emmanuel Breuillard, Ben Green, and I have just uploaded to the arXiv our paper “The structure … more →
254A, Notes 0: Hilbert's fifth problem and related topics
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wrote 9 months ago: This fall (starting Monday, September 26), I will be teaching a graduate topics course which I have … more →
The Furstenberg multiple recurrence theorem and finite extensions
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wrote 11 months ago: In 1977, Furstenberg established his multiple recurrence theorem: Theorem 1 (Furstenberg multiple re … more →
Higher order Fourier analysis
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wrote 1 year ago: I’ve just finished writing the first draft of my third book coming out of the 2010 blog posts, … more →
An incidence theorem in higher dimensions
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wrote 1 year ago: Jozsef Solymosi and I have just uploaded to the arXiv our paper “An incidence theorem in highe … more →
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