Mathematical Sciences: Topics in Operator Algebras

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Voiculescu will to continue his work in three different aspects of operator algebra theory: (i) normed-ideal perturbations of Hilbert space operators and entropic invariants of dynamical systems, (ii) II_1 factors of free groups and the noncommutative probability approach to free products, (iii)quasidiagonal C*-algebras and approximation of algebras. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These seemingly abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA.