Mathematical Sciences: Rigidity

康奈利打算研究刚性结构理论中的一些基本问题。典型的科目包括最小布线，自应力和Gale图，一般的整体刚度，以及某些对称“张拉网格”的预应力稳定性。一个被证明非常有用的基本概念是与张拉整体框架的自应力相关的能量形式。它的等级、指数和正确定性都与重要的刚性特性有关，在将来应该证明是有用的。康纳利还计划研究某些包装和覆盖问题，特别是那些与刚性有关的问题。由刚性杆组成的框架或由支撑索加固的框架的刚度的数学理论令人惊讶地适用于一般原理的分析以及明显的实际相关性。包装和覆盖问题也支持丰富的理论，并被发现与纠错码的设计相关。

R. Connelly intends to study some fundamental problems in the theory of rigid structures. Typical subjects include minimal cabling, self-stresses and Gale diagrams, generic global rigidity, and the pre-stress stability of certain symmetric "tensegrids". A basic concept that has proved surprisingly useful is the energy form associated to a self-stress for a tensegrity framework. Its rank, index, and positive definiteness are all related to important rigidity properties and should prove useful in the future. Connelly also plans to study certain packing and covering problems, particularly those related to rigidity. The mathematical theory underlying the rigidity of frameworks composed of rigid rods or of such frameworks reinforced by bracing cables is surprisingly amenable to analysis by general principles as well as of obvious practical relevance. Packing and covering problems also support a rich theory and have been found relevant to the design of error-correcting codes among other things.