Theory and applications of algebraic combinatorics

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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?