Hausdorff dimension and projections

Pertti Mattila (University of Helsinki)

Thursday, October 22, 2015 4:00 pm
MSB 109A

Hausdorff dimension is a parameter which gives us information about metric size of sets. Marstrand proved in 1954 that for sets of Hausdorff dimension s almost all orthogonal projections on lines also have Hausdorff dimension s, provided s is at most 1, and they have positive length, provided s is bigger than 1. There have been many generalizations and variations of this result. In the talk I shall discuss some of the recent ones.