Microlocal analysis and inverse problems of hyperbolic equations
报告题目(Title)：Microlocal analysis and inverse problems of hyperbolic equations
报告人(Speaker)：陈曦（剑桥大学）
地点(Place)：后主楼1129
时间(Time)：2019年12月2日 15：00-16：00
邀请人(Inviter)：徐桂香
报告摘要
Microlocal analysis studies the structure of differential operators on the cotangent bundle of the underlying space. It has seen a remarkable variety of applications across inverse problems of PDEs since 1980s. We shall look at the use of the microlocal description of the fundamental solutions to linear hyperbolic equations to the recovery of the geometry. Specifically, the following particulars will be discussed.
1. Melrose-Uhlmann's intersecting Lagrangian distributions, developed from Hörmander's Fourier integral operators, describe the fundamental solutions to linear hyperbolic equations.
2. This microlocal description is used to understand the source-to-solution map of semilinear connection wave equations and the Yang-Mills equations in terms of parallel transport associated with the connection.
3. The source-to-solution map determines a broken scattering transform, the injectivity of which solves the geometric inverse problem.
