Nodal geometry of high frequency eigenfunctions

Let $M$ be a compact Riemannian manifold, and $varphi_\lambda$ be an eigenfunction of the
Laplacian corresponding to the eigenvalue $\lambda$. The nodal geometry of $\varphi_\lambda$, when the
frequency $\lambda$ is high, seems to be a very active area of research. In this talk, we
will try to motivate a few open problems in this area and discuss (heuristically) why said problems
are challenging. We will also outline some of our recent results about the asymptotic nodal geometry
of $\varphi_\lambda$ (joint work with Bogdan Georgiev, MPIM).