Abstract: This talk will cover finished and unfinished work with Joonas during my time in Jyväskylä. I will talk about the elastic wave equation that models waves that propagate through elastic media. We are particularly interested in materials that are highly anisotropic and aim at recovering the so-called stiffness tensor, that captures the elasticity of the material, from exterior measurements. The stiffness tensor is modelled as a fourth rank tensor and in the talk I will touch upon how the tensor behaves under coordinate transformations (that maintain the symmetries of the tensor) and what information of this tensor can be recovered at the boundary. The latter builds on relatively new ideas by Joonas of using algebraic geometry as a tool, since the principal behavior of the elastic wave operator is linked to the zeros of a polynomial.
