At the interface between semiclassical analysis and numerical analysis of wave propagation problems

我们对波传播的理解是日常使用中几项重要技术的基础。例如，WiFi和移动的电话使用电磁波来传输信息，地震和医学成像中的技术使用声波、弹性波和电磁波来获取有关海底和人体的信息。在过去的几年里，研究人员一方面从纯数学的角度（没有任何应用的想法）对波动现象感兴趣的研究人员，另一方面，主要对改善波动现象在应用中的模拟方式感兴趣的研究人员（这种理解然后投入到新技术中）。这一经验揭示了波传播的理论方面和更实际的方面之间的关系的巨大未开发的潜力，这个奖学金旨在利用这一点。总体目标是（i）证明有关波传播的基本理论结果，由应用激发，（ii）使用这些理论结果来证明有关波传播如何使用计算机模拟的基本结果，解决长期存在的开放问题，并开发新的数值方法，这些方法有可能改变波传播的各种实际应用中使用的技术。

Our understanding of wave propagation underpins several important technologies in everyday use. For example, WiFi and mobile phones use electromagnetic waves to transmit information, and the technologies in seismic and medical imaging use acoustic, elastic, and electromagnetic waves to obtain information about the ocean floor and the human body. Over the last few years, the investigator has worked with, on the one hand, researchers interested in wave phenomena from a purely mathematical point of view (without any thought of applications), and, on the other hand, researchers interested primarily in improving how wave phenomena are simulated in applications (with this understanding then feeding into new technologies). This experience has uncovered huge untapped potential in the relationship between the theoretical aspects of wave propagation and the more-practical aspects, and this fellowship seeks to exploit this.The overall goals are to (i) prove fundamental theoretical results about wave propagation, motivated by applications, and (ii) use these theoretical results to prove fundamental results about how wave propagation is simulated using computers, addressing long-standing open problems and developing new numerical methods that have the potential to change the technologies used in the huge variety of practical applications of wave propagation.