In 1988, Falconer introduced the affinity dimension and showed that, under
a suitable contraction assumption, the Hausdorff and box-counting dimensions
of a typical self-affine set are equal to its affinity dimension. In 2007, Jordan,
Pollicott and Simon established an analogous result for ergodic measures, show-
ing that the Hausdorff dimensions of their images under the coding map are
equal to their Lyapunov dimensions. In this talk, I will present results on the
dimensions of orthogonal projections of typical self-affine sets and measures.
This is joint work with De-Jun Feng.