International Research Fellowship Program: Deformation Quantization and Analysis on Lie Groups

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0202132DvorskyThe International Research Fellowship Program enables U.S. scientists and engineers to conduct three to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.This award will support an eight month research fellowship by Dr. Alexander L. Dvorsky to work with Dr. Daniel Sternheimer at the University de Bourgogne in Dijon, France. Co-funding for this project comes from the Math and Physical Science Directorate's Office of Multidisciplinary Activities.Quantization is the process of forming a quantum-mechanical system starting from a classical one. There exist different methods of quantization, and Dr. Dvorsky is interested in deformation quantization. Intuitively a deformation of a mathematical object is a family of the same kind of objects depending on some parameter. An example is deforming a cummutative algebra of functions (with the ordinary product) leads to the non-commutative "star-products" suitable for quantum mechanics. This project addresses the applications of deformation quantization to the central questions of analysis on Lie groups (mathematical objects which encode the symmetries of various classical-and quantum-mechanical constructions) and Lie supergroups.The host and his laboratory at the Universite de Bourgogne have strong connections with leading research performed in France and other countries of the European Union.