Title
Algebraic geometry of boundary determination from the Dirichlet-to-Neumann map
Abstract
The Dirichlet-to-Neumann map encodes boundary measurements of displacements in an elastic medium governed by the linear elastic wave equation. We study the inverse problem of recovering, from these measurements, the stiffness tensor of the medium along the boundary. The resulting algebro-geometric questions can be addressed using spreading-out theorems from classical scheme theory. In this talk, we will explain this connection in an intuitive way to potentially inspire future applications of algebraic geometry of this kind. The talk is based on joint work with Joonas Ilmavirta, Mikko Salo, and Hjørdis Schlüter.
