Theory and applications of algebraic combinatorics

这项研究交织在一起两股，一个理论和一个应用。在理论方面，该计划探讨了代数组合学中对称函数的恒等式。这些恒等式，以及类似代数中的许多相关恒等式，在理论物理、代数几何、表示论和组合学中起着重要的作用。 因此，找到这样的身份是至关重要的所有这些科目。 在应用方面，该方案探讨了匿名网络的安全性。匿名网络--例如Tor--隐藏了关于匿名者和接收者之间关系的信息。它们已经是持不同政见者、记者和执法官员的重要通信手段，随着普通人对电子隐私的关注日益增加，它们将变得更加普遍。但它们有多安全呢？

This research weaves together two strands, one theoretical and one applied. On the theoretical side, this programme explores identities of symmetric functions from algebraic combinatorics. These identities, as well as a host of related identities in similar algebras, play a significant role in theoretical physics, algebraic geometry, and representation theory as well as combinatorics. Thus finding such identities is crucial for all these subjects. On the applied side this programme explores the security of anonymity networks. Anonymity networks--for example, Tor--conceal information about the relationship between senders and receivers. They are already a vital means of communication for political dissidents, journalists, and law enforcement officials, and as the common person's concern with electronic privacy grows, they will become more widespread. But how secure are they?