Additive combinatorics: subsets, sum-product problems, and graphs

Matt DeVos

Department of Mathematics, Simon Fraser University, Burnaby, B.C. Canada

Department of Mathematics, Simon Fraser University, Burnaby, B.C. Canada

2014/09/02 Tuesday 4pm-6pm Room 1409

Lecture 1: Sumsets and Subsequence Sums (Cauchy-Davenport, Kneser, and Erdos-Ginzburg-Ziv) (LECTURE NOTE)

2014/09/16 Tuesday 4pm-6pm Room 1409

Lecture 2: Rough Structure (Green-Ruzsa) (LECTURE NOTE)

2014/09/18 Thursday 4pm-6pm

*Room 3433*Lecture 3: Sums and Products (Elekes and Dvir) (LECTURE NOTE)

2014/09/23 Tuesday 4pm-6pm Room 1409

Lecture 4: Graphs and Sumsets (Schrijver-Seymour) (LECTURE NOTE)

I intend to give an introduction to some of the wonderful topics in the world of additive combinatorics. This is a broad subject which features numerous different tools and techniques, and is presently a hotbed of exciting research. My focus will be on the combinatorics, and I will keep things as basic as possible (I will assume nothing more than a basic background in combinatorics). I’ll begin the tour with some of the classical theorems like Cauchy-Davenport and Erdos-Ginzburg-Ziv and I will exhibit some very clean proofs of these and other results such as the Theorems of Schrijver-Seymour, Green-Ruzsa, Dvir, and Elekes. We will also discuss (but not prove) some more recent results like the Breulliard-Green-Tao Theorem.

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