Mathematical Sciences: Topics in Dynamics and Differential Topology

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The research covers a number of problems in the area of billiard dynamical systems, differential topology and the theory of knots. Particular problems include the classification of Legendrian knots in contact 3-manifolds and the classification of smooth immersed plane curves. Knot invariants arising in modern quantum field theory will also be studied. The research covers several topics which have potential applications to dynamical and and mechanical systems, and some areas of mathematical physics. Besides the mentoring of graduate students, the investigator's work is partly accessible to undergraduate students. Expository lectures and instruction to the latter are anticipated. Thus the investigator's research carries an educational component which would be in line with the categories of the current SMET initiative. ***