The Ohio State University|
Department of Mathematics
Member of the
National Academy of Sciences,
Winner of the Harvey Prize
|Week 1:||General Introduction: Fractals, trees and the various|
notions of dimension. The dynamics of changing scale.
|Week 2:||Rudiments of ergodic theory: Ergodic theorems and recurrence theorems|
|Week 3:||Markov trees, random walks on spaces of measures on Euclidean space.|
First applications of ergodicity.
|Week 4:||Homogeneous fractals and their properties.|
|Week 5:||Geometric Ramsey theory for fractals and sets of positive logarithmic|
density. Recurrent measures on Euclidean space.