Singular sets for differential equations

In this talk, we shall discuss a class of singular sets associated with differential equations. Such sets are simply the critical nodal sets for elliptic equations of the second order. They form the singular parts of the nodal sets. We shall show that these sets are rectifiable of codimension 2 under very few assumptions on the coefficients of equations. We shall also discuss how to obtain measure estimates of these sets. Methods are from geometric measure theory and several complex variables.