Analysis Seminar: Observability of the heat equation from very small sets

Abstract: An observation set is a set from which the entire phenomenon may be observed, in the sense that the data may (in some sense) be continuously reconstructed from its observation on this small set. In this talk, we will discuss recent developments in understanding the dimension of observation sets for the heat equation. Then, we will see how other geometric considerations related to the nodal sets of eigenfunctions can refine these results in certain special cases.