Multi-fractal spectrum of planar harmonic measures

We will begin with defining the concepts of harmonic measure and different notions of dimensions. We will then connect those notions with what is called multi-fractal spectrum. Next, we will discuss finer features of the relationship between those dimensions. Lastly, we will define the universal counterparts and discuss an approximation theorem, showing the importance of domains arising from multifractal formalism. This is a developing story, based on a joint work with I. Binder.