Mathematical Sciences: Topological Knot Theoretic Connections

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This research will focus on the Jones polynomial, an invariant in knot theory, and will use a new topological approach which replaces the algebraic and combinatorial techniques with a simpler geometric method. This research should give a deeper understanding of a problem posed in one field by investigating it in the language of other areas of connected knowledge. The study of the relations between this new geometric approach and those already established should lead to a better understanding of all of this theory and provide a unified approach. Knot theory is an area of research in topology and algebra that has a variety of applications to mathematical biology in the description of DNA and to theoretical physics; in particular, conformal field theory and statistical mechanics.