507- Plünnecke inequalities and sumset estimates

February 10, 2011

George Petridis, a student of Gowers, has found very nice new arguments for the Plünnecke-Ruzsa sumset inequality (If A is a finite subset of an Abelian group G, and {}|A+A|\le C|A|, then {}|kA-lA|\le C^{k+l}|A| for any k,l\in{\mathbb N}) and for the Plünnecke graph inequalities.

In lecture we went through the nice standard argument. But the new proofs are significantly simpler. For example, the graph inequalities are no longer needed for the sumset ones, and Menger’s theorem is no longer needed fro the graph inequalities. Gowers has posted the nice proof in his blog, with links to Petridis’s papers on the ArXiv.


507- Problem list (IV)

January 21, 2011

For Part III, see here.

(Many thanks to Robert Balmer, Nick Davidson, and Amy Griffin for help with this list. If you have corrections/updates, please email me. Sorry for the delay with posting this.)


507- Problem list (III)

January 20, 2011

For Part II, see here.

(Many thanks to Robert Balmer, Nick Davidson, and Amy Griffin for help with this list.)

Part IV.


507 – Homework 3

October 24, 2010

This set is due Monday, November 8.

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507 – Problem list (II)

October 16, 2010

For the beginning of the list, see here.

Part III.


507 – Homework 2

September 29, 2010

This set is due Monday, October 18.

Read the rest of this entry »


507 – Problem list (I)

September 21, 2010

This is the list of “problems of the day” mentioned through the course.

(Thanks Nick Davidson and Summer Hansen.)

Part II.