# Dimensions of the two-valued sets of the 2D GFF

The two-valued sets of the two-dimensional Gaussian free field
(GFF) are local sets such that the associated harmonic function takes
only two values. In this talk, we describe how to compute the almost
sure Hausdorff dimension of these sets. A central tool is the imaginary
multiplicative chaos, that is, the random element exp(ic h(z)), where h
is a GFF . The talk is based on joint work with Avelio Sepulveda and
Fredrik Viklund.