DMS-9623314 PI: Nagy Kansas State University Nagy will investigate rigidity phenomena in C*-algebraic deformation quantization. In order to address such problems, Nagy plans to use and develop homological techniques adequate for the classification of certain classes of C*-algebras. One motivation of this research is the recent worldwide interest in the promising new theory of quantum groups which links together several branches of mathematics and is closely related to mathematical physics. Another motivation and inspiration for this project is the development in the K-theory of C*-algebras in connection with non-commutative geometry. The area of mathematics for this project has its basis in the theory of algebras of operators on Hilbert spaces. The study of operator algebras was initiated in the 1930's by John von Neumann in order to provide a mathematical framework for quantum mechanics. Due to a broad range of applications, operator algebras are presently one of the most dynamic fields in mathematics. For example, the remarkable interactions of operator algebras with knot theory, discovered by Vaughan Jones in the 1980's, lead to interesting applications to the study of the DNA molecules. Due to their fundamental role in non-commutative geometry, in quantum probability theory, and in conformal quantum field theory, operator algebras have become increasingly important in physics.
