An introduction to higher energies and sumsets

Abstract

These notes basically contain a material of two mini--courses which were read in Göteborg in April 2015 during the author visit of Chalmers & Göteborg universities and in Beijing in November 2015 during "Chinese--Russian Workshop on Exponential Sums and Sumsets". The article is a short introduction to a new area of Additive Combinatorics which is connected which so--called the higher sumsets as well as with the higher energies. We hope the notes will be helpful for a reader who is interested in the field.

32 pages

References in corpus (7)

• Some new inequalities in additive combinatorics
• Energies and structure of additive sets
• On sums of Szemerédi--Trotter sets
• Structure in additively nonsmoothing sets
• Some applications of W. Rudin's inequality to problems of combinatorial number theory
• Sets with few distinct distances do not have heavy lines
• Kakeya-type sets in finite vector spaces

Cited by in corpus (1)

• On ${\ell }_4:{\ell }_2$ ratio of functions with restricted Fourier support