Problems in Extremal and Geometric Combinatorics

极值和几何组合问题

• 批准号: 2154063
• 负责人: Boris Bukh
• 金额: $ 24万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2154063&HistoricalAwards=false
• 关键词: Problems; Extremal; Geometric; Combinatorics

The development of extremal and geometric combinatorics has been informed by questions in a number of areas of mathematics, computer science and other disciplines. The aim of the project is both to develop general combinatorial tools of wide applicability and to solve specific combinatorial problems. Graduate and undergraduate students will be trained during this project.The specific problems to be tackled include algebraic and geometric questions related to Turan problems and Ramsey theory. Particular attention will be devoted to algebraic constructions. The aim here is to understand the apparent rigidity of many known constructions in the area, and develop more general techniques. It is expected that this will result in forging the connections between finite geometry and extremal combinatorics closer, enriching both areas. The project also considers several topics related to words and subsequences, as well as discrepancy theory. The potential impact includes better error-correcting codes and numerical algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

极值组合学和几何组合学的发展受到数学、计算机科学和其他学科许多领域的问题的启发。该项目的目的是开发具有广泛适用性的通用组合工具并解决特定的组合问题。该项目将对研究生和本科生进行培训。具体要解决的问题包括与图兰问题和拉姆齐理论相关的代数和几何问题。将特别关注代数构造。这里的目的是了解该领域许多已知结构的明显刚性，并开发更通用的技术。预计这将导致有限几何和极值组合之间的联系更加紧密，丰富这两个领域。该项目还考虑了与单词和子序列以及差异理论相关的几个主题。潜在影响包括更好的纠错码和数值算法。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。