Conference: Geometric and Asymptotic Group Theory with Applications

会议：几何和渐近群理论及其应用

• 批准号: 0613035
• 负责人: Vladimir Shpilrain
• 金额: $ 2.4万
• 依托单位: CUNY City College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-08-01 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0613035&HistoricalAwards=false
• 关键词: Conference; Geometric; Asymptotic; Group; Theory

This conference will be devoted to the study of a variety of topics in geometric and combinatorial group theory, with special emphasis on asymptotic and probabilistic methods and their applications. More specifically, this includes: group actions, quasi-isometries, isoperimetric functions, growth, asymptotic invariants, random walks, algorithmic problems, etc.Applications will be emphasized, especially those concerning complexity theory and information security, in particular theoretical cryptography. Cryptographic protocols have become a key element of information systems, protecting data and communications to ensure confidentiality, integrity and authenticity of data. While most symmetric key systems have relatively modest mathematical requirements, asymmetric or public key cryptosystems have become increasingly mathematically sophisticated, and, in particular, the emerging ``non-commutative cryptography" exploits various properties of non-commutative infinite groups in very non-trivial ways. Building a solid mathematical foundation for the use of infinite groups in cryptography inevitably involves operating with various asymptotic and statistical aspects of infinite groups, and this iswhere modern group theory finds its important applications. More information an be found on the conference web sitehttp://www.epsem.upc.edu/~gagta/

本次会议将致力于研究各种主题的几何和组合群论，特别强调渐近和概率方法及其应用。更具体地说，这包括：组行动，准等距，等周函数，增长，渐近不变量，随机游走，算法问题等应用将被强调，特别是那些有关复杂性理论和信息安全，特别是理论密码学。密码协议已成为信息系统的关键要素，保护数据和通信，以确保数据的机密性、完整性和真实性。虽然大多数对称密钥系统具有相对适度的数学要求，但非对称或公钥密码系统在数学上变得越来越复杂，特别是新兴的“非交换密码学”以非常重要的方式利用了非交换无限群的各种性质。为在密码学中使用无限群建立坚实的数学基础不可避免地涉及到无限群的各种渐近和统计方面的操作，这就是现代群论的重要应用。更多的信息可以在会议网站上找到http：www.epsem.upc.edu/~gagta/