Inverse obstacle scattering problems for acoustic and electromagnetic waves

The talk is concerned with the inverse problems related to acoustic and electromagnetic scattering. We shall focus on unique recovery of the shape of obstacles of polygonal and polyhedral types, from the knowledge of far-field patterns coming from a single incident plane wave for acoustic and electromagnetic waves respectively. The Problem of uniqueness mentioned above have been open for a long time since Lax and Philips monograph 1967. We shall discuss the results obtained when the scatterers have specific shapes. We will first prove a ‘non-point to point’ reflection principle for the Helmholtz and Maxwell’s equations with impedance boundary conditions and use it to prove the uniqueness results by extending the scattered field analytically inside the scatterers. 

The talk is based on joint work with Guang-Hui Hu, Nankai University, China and  Jiaqing Yang, Xi’an Jiaotong University, China.

Manmohan Vashisth is a faculty member in the Department of Mathematics at the Indian Institute of Technology, Ropar. His research focuses on inverse problems, especially those involving partial differential equations (PDEs), geometric inverse problems, integral geometry and inverse scattering problems. He received his PhD in Mathematics from the Tata Institute of Fundamental Research (TIFR) Centre for Applicable Mathematics (CAM), Bangalore.