Conference: Geometric and Asymptotic Group Theory with Applications

这次会议将致力于研究几何和组合群论中的各种主题，特别强调渐近和概率方法及其应用。具体包括：群作用、拟等距、等周函数、增长性、渐近不变量、随机游动、算法问题等，重点介绍其在复杂性理论和信息安全方面的应用，特别是理论密码学。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。虽然大多数对称密钥系统对数学要求相对较低，但非对称或公钥密码系统在数学上已经变得越来越复杂，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运算，这就是现代群论发现其重要应用的地方。更多信息可以在会议的网站http://www.epsem.upc.edu/~gagta/上找到

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/