交叉研究的感悟

本文是基于北京大学"许宝騄讲座"(2019/3/22)及随后在各地的报告扩充而成.开头是受惠于许宝騄先生的一些回忆;末尾是感谢北京大学一批老师几十年来的支持和帮助.中间的主题部分先给出个人交叉研究的概述.然后从来自计算的挑战,进入一年多来笔者关于具有实谱的复矩阵理论的研究.这涉及计算、概率、统计力学和量子力学等领域.随后介绍算法方面的最新进展,此乃概率论与计算交叉的又一案例.作为结束,也略述交叉研究的感悟.

Interpretation of Cross-disciplinary Research

This paper is based on "Pao-Lu Hsu’s lecture"(2019/3/22) at Peking University and the subsequent expansion of his reports.It begins with some recollections benefited of the author from Professor Hsu,and ends with thanking to a group of professors at Peking University for their support and help over the past decades.The middle part is the theme of the talk.It gives first an overview of personal cross research.Then,from a challenge of computing,the author reports on the study looking for a larger class of complex matrices which have real spectrum.This was done mainly in the last year.It involves the fields of computation,probability,statistical mechanics and quantum mechanics Next,the paper introduces the latest development of algorithms,which is another illustration of the intersection between probability theory and computational mathematics.As the end,it also outlines the understanding of the cross study.