Balazs Barany (Budapest):  
Dimension of planar self-affine measures with application to Birkhoff and Lyapunov spectra.
 
Abstract: For affine iterated function systems on the plane, under the assumption of strong irreducibility and strong open set condition, we prove that the Hausdorff dimension of the attractor is equal to the affinity dimension, and similarly for self-affine measures, the dimension is equal to the Lyapunov dimension. Under the assumptions above, we calculate the Birkhoff spectrum of continuous potentials and the Lyapunov spectrum. The talk is based on two papers, which are joint works with Michael Hochman, Ariel Rapaport and Thomas Jordan, Antti Käenmäki, Micha³ Rams.