As part of the MSU Mathematics Lecture Series, Professor Jacob Rezac, from the University of Delaware will be presenting : “Inverse Wave Scattering Problems and Transmission Eigenvalues”. This presentation is scheduled for Wednesday April 13th at 3PM in Cheek 301. Everyone is welcome to attend!
In an inverse scattering problem, we attempt to reconstruct information about unknown objects based on how waves (e.g., acoustic or electromagnetic) scatter off of them. One approach to solving this problem, the linear sampling method, has proven to be a fast and reliable technique for reconstructing an obstacle’s shape and location. The success of the linear sampling method depends on the behavior of solutions to a non-self-adjoint eigenvalue problem called the transmission eigenvalue problem. In this talk, we discuss this relationship and give new results on the existence and behavior of solutions to the transmission eigenvalue problem. These results make use of the theory of complex analysis and the theory of elliptic partial differential equations.