We talk about the Hausdorff measure of level sets of the fields, say length of level lines of a planar field. Given two coupled stationary fields  $f_1, f_2$ , we estimate the difference of Hausdorff measure of level sets in expectation, in terms of $C^2$-fluctuations of the field $F=f_1-f_2$. The main idea in the proof is to represent difference in volume as an integral of mean curvature using the divergence theorem. This approach is different from using the Kac-Rice type formula as the main tool in the analysis. 

I will discuss how to place conformal boundary conditions on free higher derivative theories of scalars and spinors as well as the zoo of boundary renormalization group flows that connect the different boundary conditions.  Historically, there are connections to Poisson’s ratio and classical equations governing the bending of thin steel plates.  As these higher derivative theories are often invoked in the context of cosmology, there may be cosmological applications for the boundary conditions discussed here.