Probing the earth and the universe with microlocal analysis

这个项目的目的是利用微局域分析的理论来确定通过观察波的传播可以恢复多少关于地球和宇宙的信息量。除了在地震成像和宇宙学方面的应用外，这个项目还将在微分几何和动力系统领域产生新的知识。这将通过用微分几何的语言表述层析成像问题并引入新的分析技术来研究它们来实现。该项目的预期结果将是洛伦兹几何和黎曼几何中的新刚性类型结果。在地震和宇宙学成像方面也有可能产生下游影响。

This project aims to use the theory of microlocal analysis to determine the amount of information one can recover about the earth and the universe by making observations on wave propagation. In addition to applications to seismic imaging and cosmology, this project will generate new knowledge in the field of differential geometry and dynamical systems. This will be accomplished by formulating the tomography problem in the language of differential geometry and introduce new analysis techniques to study them. Expected outcome of this project will be new rigidity type results in Lorentzian and Riemannian geometry. There is also the potential for downstream impacts in seismic and cosmological imaging.