Mathematical Sciences: Research in Circle Packings, Quasiconformal Geometry and Low Dimensional Geometric Topology

主要研究人员将研究共形模和不可压缩流动的能量，以及圆填充和黎曼曲面几何之间的关系。第一个项目涉及调查节点类型的场线如何限制能量的任意减少。第二个项目将是先前关于六边形包装格式导数收敛的工作的继续。首席调查员将在几何复杂分析领域开展两个项目。第一个涉及对流体流动行为的研究。特别是，他将分析当流线打结时，流动失去能量或减速的方式。第二个项目涉及如何用更小的圆填充圆与保形复分析之间的关系。

The principal investigator will study conformal moduli and the energy of incompressible flows, and the relationship between circle packings and the geometry of Riemann surfaces. The first project involves an investigation into how knot types of field lines restrict arbitrary decreases in the energy. The second project will be a continuation of earlier work on the convergence of derivatives for hexagonal packing schemes. The principal investigator will carry out two projects in the area of geometric complex analysis. The first involves a study of the behavior of fluid flow. In particular, he will analyze the manner in which a flow loses energy or slows down when flow lines are knotted. The second project involves the relationship between how a circle can be packed with smaller circles, and aspects of conformal complex analysis.