Mathematical Sciences: Presidential Young Investigator Award

这个总统青年调查员奖支持 普林斯顿的弗雷德里克·比恩教授的数学著作 大学比恩博士的研究目标是 数学和科学中的几个问题，他的专长是 群的表示理论在数学方面，他将致力于 在决定哪些非线性微分方程可以 通过逆谱变换进行积分。在理论 计算机科学，Bien博士将致力于扩展图形， 可以模拟理想的通信网络。他还将运用他的 神经网络领域的知识。 群论开始于世纪早期， 描述可能连续进行的操作，以及 同样，当顺时针旋转90度时， 逆时针旋转90度。李群是 在那个世纪后期， 挪威数学家Sophus Lie，他对 关于微分方程的最基本的问题。 一百年后的今天，群论在现代 科学，以及李群在许多分支中的效用， 数学和物理学一样，一直没有减少。

This Presidential Young Investigator Award supports the mathematical work of Professor Frederic Bien of Princeton University. Dr. Bien's research aim is to bring to bear on several problems in mathematics and science his expertise in the representation theory of groups. Within mathematics, he will work on deciding precisely which nonlinear differential equations can be integrated by the inverse spectral transform. In theoretical computer science, Dr. Bien will work on expanding graphs, which may model ideal communication networks. He will also apply his knowledge to the field of neural networks. Group theory began in the early nineteenth century as a description of operations that might be done successively, and also undone, as a ninety-degree clockwise rotation is undone by the ninety-degree counterclockwise rotation. Lie groups were developed in the late part of that century by the path breaking Norwegian mathematician Sophus Lie, who was interested in the most fundamental questions concerning differential equations. Now, one hundred years later, group theory pervades modern science, and the utility of Lie groups in many branches of mathematics, as well as in physics, has continued undiminished.