Dimension theory of stationary measures

I will try to give a broad survey of the dimension theory of stationary measures (self-similar, self-affine, Furstenberg measure,…), and the various tools that have played a role in the theory: Fourier analytic techniques in the first half of the 20th century, Algebraic examples from the mid-century, transversality methods in the 1990s, and the recent additive combinatorics methods. I will focus in particular on results related to Bernoulli convolutions, culminating in the striking recent resuls of Varju, and if time permits I will discuss progress on non-conformal systems, which will be discussed in more detail in the analysis seminar on Thursday.