Dilations and Higher Rank Operator Algebras - with Applications

This project has several strands with a common theme of `dilation', whereby a mathematical object is viewed as a part of a larger, but simpler, construction. By bringing together experts, all of whom have proven records in collaboration as well as research, our plan is to make progress in the following areas.* Analytic Toeplitz algebras: classification of subalgebras, development of representation and dilation theory.* Noncommutative dynamics: computation of invariants and classification of cocycles.* Quantum computation and information: mathematical problems such as the estimation of states.Keen interaction of the proposed visitors with research students, postdocs, other visitors and colleagues of the investigators, for example through seminars, is also anticipated.