Conference: Geometric and Asymptotic Group Theory with Applications, September 15-19, New York, NY

会议：几何和渐近群理论及其应用，9 月 15 日至 19 日，纽约州纽约

• 批准号: 0805552
• 负责人: Vladimir Shpilrain
• 金额: $ 2.5万
• 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: 2008
• 资助国家: 美国
• 起止时间: 2008-08-01 至 2009-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0805552&HistoricalAwards=false
• 关键词: Conference; Geometric; Asymptotic; Group; Theory

The conference on "Geometric and Asymptotic Group Theory with Applications" will be devoted to the study of a variety of topicsin geometric and combinatorial group theory, with special emphasis on asymptotic and probabilistic methods and their applications.More specifically, the topics include: group actions, quasi-isometries, isoperimetric functions, growth, asymptotic invariants, randomwalks, algorithmic problems, etc. Applications will be emphasized, especially those concerning complexity theory and information security. Building a solid mathematical foundation for the use of infinite groups in cryptography will inevitably involve operating with various asymptotic and statistical aspects of infinite groups, and this is where modern group theory finds its important applications.What makes this conference stand out compared to other conferences on geometric and/or asymptotic group theory is the emphasis onapplications to other areas of science and to real-life problems. More specifically, we are going to emphasize applications thatconcern complexity theory and information security, in particular cryptography. Cryptography and cryptographic protocols have becomea key element of information systems, protecting data and communications to ensure confidentiality, integrity and authenticityof data. While most symmetric key systems (block ciphers such as DES and AES and stream ciphers) have relatively modest mathematical requirements, asymmetric or public key systems, as well as cryptographic protocols, have become increasingly mathematically sophisticated, and, in particular, the emerging "non-commutative cryptography" exploits various properties of non-abelian infinite groups in very non-trivial ways.

The conference on "Geometric and Asymptotic Group Theory with Applications" will be devoted to the study of a variety of topicsin geometric and combinatorial group theory, with special emphasis on asymptotic and probabilistic methods and their applications.More specifically, the topics include: group actions, quasi-isometries, isoperimetric functions, growth, asymptotic invariants, randomwalks, algorithmic问题等。将强调应用程序，尤其是那些有关复杂性理论和信息安全的应用程序。为在密码学中使用无限群体的使用建立坚实的数学基础，将不可避免地涉及与无限群体的各种渐近和统计方面的运作，这是现代群体理论找到其重要应用的地方。与几何学和/或渐近群体理论相比，这次会议与其他方面的其他会议相比，与其他领域相比，与其他领域相比，与其他领域相比，与其他领域相比，与其他领域相比。更具体地说，我们将强调将复杂性理论和信息安全性，特别是密码学的应用程序。 加密和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保密性，完整性和真实性数据。 While most symmetric key systems (block ciphers such as DES and AES and stream ciphers) have relatively modest mathematical requirements, asymmetric or public key systems, as well as cryptographic protocols, have become increasingly mathematically sophisticated, and, in particular, the emerging "non-commutative cryptography" exploits various properties of non-abelian infinite groups in very non-trivial ways.