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/

这次会议将致力于研究几何和组合群体理论的各种主题，并特别强调渐近和概率方法及其应用。更具体地说，这包括：小组动作，准静态，等法功能，增长，渐近不变，随机步行，算法问题等。应用程序将被强调，尤其是那些有关复杂性理论和信息安全性的人，特别是理论上的密码。加密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。尽管大多数对称关键系统都有相对适度的数学要求，但不对称或公钥密码系统在数学上变得越来越复杂，尤其是新兴的``非公开的密码学''利用各种非某种群体在非专业的群体中涉及的各种群体的各种属性。无限群体的渐近和统计方面，这是现代群体理论的重要应用。