Mathematical Sciences: Presidential Young Investigator Award

这个总统青年研究者奖支持普林斯顿大学弗雷德里克·拜恩教授的数学工作。Bien博士的研究目标是将他在群体表示理论方面的专业知识应用于数学和科学中的几个问题。在数学方面，他将致力于精确地决定哪些非线性微分方程可以通过谱反变换进行积分。在理论计算机科学方面，拜恩博士将研究扩展图，这可能是理想通信网络的模型。他还将把他的知识应用到神经网络领域。群论开始于19世纪早期，它描述了可以连续完成的操作，也可以撤销，就像90度的顺时针旋转被90度的逆时针旋转撤销一样。李群是在19世纪后期由开创性的挪威数学家索菲斯·李发展起来的，他对微分方程的最基本问题很感兴趣。一百年后的今天，群论在现代科学中无处不在，李群在数学和物理学的许多分支中的应用也丝毫未减。

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.