Ian Morris

A Falconer-type theorem for projections of self-affine sets

A landmark theorem of Falconer from 1988 gives an expression for the Hausdorff dimension of a self-affine set with typical translations, subject to a mild additional contraction condition. I will present an extension of this result which characterises the dimensions of the projected images of these sets. I will give algebraic criteria for these sets to admit nontrivial varieties of exceptional projections in the sense of Marstrand's theorem, and for their natural invariant measures to admit projections which are not exact-dimensional. This is joint work with Çağrı Sert.