Mathematical Sciences: Topics in Modern Analysis

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Rieffel will continue his investigation of C*-algebraic quantization. Topics to be studied include quantization and quantum groups, aspects of quantum topology and differential geometry, and harmonic analysis on Lie groups. Attention will also be given to relationships with applications in such areas as quantum mechanics and field theory, and signal processing and pattern recognition. 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.