Additive Combinatorics : Winter 2007
نویسندگان
چکیده
منابع مشابه
Selected Results in Additive Combinatorics: An Exposition (Preliminary Version)
We give a self-contained exposition of selected results in additive combinatorics over the group GF (2)n = {0, 1}n. In particular, we prove the celebrated theorems known as the Balog-Szemeredi-Gowers theorem (’94 and ’98) and the Freiman-Ruzsa theorem (’73 and ’99), leading to the remarkable result by Samorodnitsky (’07) that linear transformations are efficiently testable. No new result is pro...
متن کاملSelected Results in Additive Combinatorics: An Exposition
We give a stripped-down, self-contained exposition of selected results in additive combinatorics over the vector space F2, leading to the result by Samorodnitsky (STOC 2007) stating that linear transformations are efficiently testable. In particular, we prove the theorems known as the Balog-Szemerédi-Gowers theorem (Combinatorica 1994 and GAFA 1998) and the Freiman-Ruzsa theorem (AMS 1973 and A...
متن کاملGroups in Combinatorial Number Theory
In combinatorial number theory, there are many topics related to group structure. Even for abelian or cyclic groups, there are some very challenging unsolved conjectures. In this talk we give a survey of problems, results and methods in several fields of combinatorial number theory. The topics include sumsets in additive combinatorics, Snevily’s conjecture and Latin transversals, covers of the ...
متن کاملAn Introduction to Additive Combinatorics
This is a slightly expanded write-up of my three lectures at the Additive Combinatorics school. In the first lecture we introduce some of the basic material in Additive Combinatorics, and in the next two lectures we prove two of the key background results, the Freiman-Ruzsa theorem and Roth’s theorem for 3-term arithmetic progressions. Lecture I: Introductory material 1. Basic Definitions. 2. I...
متن کاملProof of the Sum - Product Theorem
These are notes from a mini course on additive combinatorics given in Princeton University on August 23-24, 2007. The lectures were Boaz Barak (Princeton University), Luca Trevisan (University of California at Berkeley) and Avi Wigderson (Institute for Advanced Study, Princeton). The notes were taken by Aditya Bhaskara, Arnab Bhattacharyya, Moritz Hardt, Cathy Lennon, Kevin Matulef, Rajsekar Ma...
متن کامل