Mathematical Sciences: Presidential Young Investigator Award

这项总统青年研究人员奖支持普林斯顿大学弗雷德里克·比恩教授的数学工作。边博士的研究目标是将他在群表示理论方面的专长运用到数学和科学的几个问题上。在数学领域，他将致力于精确地决定哪些非线性微分方程可以通过逆谱变换进行积分。在理论计算机科学方面，边博士将致力于扩展图形，这可能会为理想的通信网络建模。他还将把自己的知识应用到神经网络领域。群论起源于十九世纪初，用来描述既可以连续完成又可以撤消的运算，因为90度顺时针旋转被90度逆时针旋转所撤消。李群是由开创性的挪威数学家索菲斯·李在那个世纪后半叶发展起来的，他对关于微分方程的最基本的问题感兴趣。一百年后的今天，群论弥漫在现代科学中，李群在数学的许多分支中的作用，以及在物理学中的作用，仍然没有减少。

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.