Mathematical Sciences: Quantum Groups and Related Topics

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This research is concerned with the theory of quantum groups. The theory of quasitriangualar Hopf Algebras, particularly calculations of certain invariants of 3- manifolds derived from finite dimensional Hopf algebras and conformal field theory, provides the focus for the project. Quantum groups are a new area of research for both mathematicians and physicists. On the mathematical side it combines three of the oldest areas of "pure" mathematics, algebra, analysis and geometry, yet it is of great interest to physicists working in conformal quantum field theory.