Additive Combinatorics

加法组合学

• 批准号: 261014-2013
• 负责人: Solymosi, Jozsef
• 金额: $ 2.11万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=525117
• 关键词: Additive; Combinatorics

My primary field of research is additive combinatorics. This relatively new area of mathematics is concerned about the additive or multiplicative structure of subsets of groups with small sumset or product set. The sumset of a set is formed by the pairwise sums of elements of the set. (In a product set we take the pairwise products.) Additive combinatorics has strong connections to number theory, harmonic analysis, ergodic theory, and theoretical computer science. I am interested in the geometry behind some of the problems in additive combinatorics.

我的主要研究领域是加法组合学。这个相对较新的数学领域关注的是具有小和集或积集的群的子集的加法或乘法结构。一个集合的和集是由该集合的元素的两两和构成的。(In一个产品集，我们采取成对产品。）加法组合学与数论、调和分析、遍历理论和理论计算机科学有着密切的联系。我对加法组合学中一些问题背后的几何学很感兴趣。