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- ItemThe Kadison-Singer problem(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Valette, AlainIn quantum mechanics, unlike in classical mechanics, one cannot make precise predictions about how a system will behave. Instead, one is concerned with mere probabilities. Consequently, it is a very important task to determine the basic probabilities associated with a given system. In this snapshot we will present a recent uniqueness result concerning these probabilities.
- ItemDirichlet Series(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) McCarthy, John E.Mathematicians are very interested in prime numbers. In this snapshot, we will discuss some problems concerning the distribution of primes and introduce some special infinite series in order to study them.
- ItemOperator theory and the singular value decomposition(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Knese, GregThis is a snapshot about operator theory and one of its fundamental tools: the singular value decomposition (SVD). The SVD breaks up linear transformations into simpler mappings, thus unveiling their geometric properties. This tool has become important in many areas of applied mathematics for its ability to organize information. We discuss the SVD in the concrete situation of linear transformations of the plane (such as rotations, reflections, etc.).