Mathematical Sciences: Quantized Analysis

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Effros, Popa, and Takesaki will continue their investigations into operator algebra theory and its applications which can be phrased as "Quantized Analysis." Quantized Analysis is a key to understanding quantum phenomenon in mathematics and physics. Effros will continue his study of operator space analysis which is essential for building an analytic theory of quantum groups. Popa will continue his work on subfactor analysis based on his successful classification of amenable subfactors. Takesaki will continue his project on the cocycle conjugacy analysis of group actions on von Neumann 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 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, and they are of fundamental importance in noncommutative geometry, which is becoming increasingly important in physics.