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Operator algebras and single operators via dynamical properties of dual objects (OperaDynaDual)
Start date: Oct 1, 2014, End date: Sep 30, 2016 PROJECT  FINISHED 

The project lies at the intersection of operator algebras, operator theory and dynamical systems, with elements of experimental mathematics and applications to noncommutative structures, completely positive dynamics, spectral analysis of functional operators, and potentially to the theory of functional-differential equations and quantum physics. It is centered around a development of an innovative powerful mathematical apparatus based on a construction of objects (of both dynamical and combinatorial nature) dual to semigroups of C*-correspondences over generically noncommutative algebras. This will allow a detailed analysis, of vast class of objects defined in terms of generators and relations, inaccessible through the existing methods. This specifically concerns algebras arising recently in connection with number and ring theory, thermodynamical phenomena, quantum spaces, quantum field theory and many more.The envisaged applications are broadly related to the analysis of quantum structures and evolutions of systems modeling complicated physical processes containing both dynamical contributory factors and interaction with outer media, e.g. the process of motion and transformation of particles. The asymptotic and ergodic properties of such systems are described by spectral properties of the appropriate operators. A substantial contribution to the theory of the latter on the basis of the elaborated general results and scientific computing is expected to be achieved.The project will integrate the fellow with an excellent Scandinavian scientific network of world leaders in crossing the boundaries between operator algebras and other fields. It will also allow cooperation with a number of visiting experts from outside the ERA. The research outputs and developed innovative methods of analysis will bring to the ERA a unique expertise of great impact and scientific value, with a wide range of potential interdisciplinary applications.

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