演讲内容：工程与数学融通共进

Abstract: The first part of this talk concerns some perspectives on how an engineer could learn mathematics by sticking to several key principles of engineering. As an example, I will take complex numbers to show how some seemingly esoteric mathematics can be brought down-to-earth by proper engineering. The second part of this talk contains some examples on how mathematics could help fluid mechanics. I will briefly introduce some of my research on numerically simulating incompressible flows with irregular and moving boundaries. This talk is intended to a wide audience: one will be able to understand (and hopefully also enjoy) the talk provided that she can do arithmetic and know what trigonometric functions are.

张庆海，清华大学工学学士及工学硕士，美国康奈尔大学（Cornell University）博士。曾在美国劳伦斯伯克利国家实验室（Lawrence Berkeley National Lab）从事博士后研究并曾在美国犹他大学（University of Utah）数学系担任科研助理教授。2015年获得国家级青年人才项目支持，2016年初起任浙江大学数学学院教授、计算数学系主任。主要研究方向为动边界不可压流体的理论建模和数值计算，工作聚焦点为界面追踪和高阶有限体积方法。研究的核心理念是在界面问题中充分运用几何和拓扑的手段来解决几何和拓扑的问题，代表性工作有：建立了一个界面追踪及其数值方法的理论分析框架，提出了四阶及以上精度的界面追踪和曲率估计算法，并发展了一系列时空一致四阶精度的并行自适应有限体积法。 在《SIAM Review》、《Mathematics of Computation》、《SIAM Journal on Numerical Analysis》、《SIAM Journal on Scientific Computing》、《PNAS》、《Journal of Computational Physics》、《Computer Methods in Applied Mechanics and Engineering》等学术刊物上发表论文30多篇。