Note: this post is of a particularly technical nature, in particular presuming familiarity with nilsequences, nilsystems, characteristic factors, etc., and is primarily intended for experts. 1,362 more words

## Tags » Nilsequences

#### An informal version of the Furstenberg correspondence principle

One of the basic objects of study in combinatorics are finite strings or infinite strings of symbols from some given alphabet , which could be either finite or infinite (but which we shall usually take to be compact). 3,613 more words

#### 254B, Notes 6: The inverse conjecture for the Gowers norm II. The integer case

In Notes 5, we saw that the Gowers uniformity norms on vector spaces in high characteristic were controlled by classical polynomial phases .

Now we study the analogous situation on cyclic groups . 5,378 more words

#### An arithmetic regularity lemma, an associated counting lemma, and applications

Ben Green, and I have just uploaded to the arXiv our paper “An arithmetic regularity lemma, an associated counting lemma, and applications“, submitted (a little behind schedule) to the 70th birthday conference proceedings for Endre Szemerédi. 972 more words

#### The Mobius function is strongly orthogonal to nilsequences

Ben Green and I have just uploaded to the arXiv our paper, “The MÃ¶bius function is asymptotically orthogonal to nilsequences“, which is a sequel to our earlier paper “ 1,109 more words