Project description 
This project is concerned with the mathematical understanding of critical systems in two dimensions, in particular, in the case that systems live on multiply connected domains. As a specific example of such a critical system, we concentrate on a model called Gaussian free field (GFF). A central issue under this setting is to determine the probability law of the random curve associated to the GFF typically as the contour line, or the flow line of a vector field defined in terms of the GFF. In this
project, we especially consider the case that candidates for such random curves are given by an annulus Schramm–Loewner evolution or a Komatu–Loewner evolution and intend to prove that these candidates are indeed flow lines of GFFs. The anticipated results will be a significant step towards the full understanding of the conformal invariance of critical systems.
This project is carried out at Department of Mathematics and Systems Analysis, Aalto University. 
