Mathematical Sciences: Topics in Dynamics and Differential Topology

研究内容涉及台球动力系统、微分拓扑和节理论等领域的许多问题。具体问题包括接触3流形中Legendrian结点的分类和光滑浸入平面曲线的分类。在现代量子场论中出现的结不变量也将被研究。该研究涵盖了几个有潜在应用于动力和机械系统的主题，以及数学物理的一些领域。除了指导研究生之外，研究者的工作部分面向本科生。解释性讲座和指导后者是预期的。因此，研究者的研究带有教育成分，这将符合当前SMET倡议的类别。＊＊＊

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. ***