# Dynamics seminar: Balasz Barany (BME) On the Ahlfors regularity of planar self-affine sets

**Abstract**: In this talk, we study the Ahlfors regularity of planar self-affine sets under natural conditions: strong separation condition, strong irreducibility and proximality. Not surprisingly, if the dimension is strictly larger than 1, the set is never Ahlfors regular. In case if the dimension is less than or equal to 1 under the extra condition of dominated splitting, we show that the Ahfors regularity is equivalent to the positive proper dimensional Hausdorff measure and to positive proper dimensional Hausdorff measure of the projections in every Furstenberg direction.