Title: Protection Statistics in Rooted Trees

Abstract: For the first part of the talk, we will look at different classes of unlabeled simply generated rooted trees and study the asymptotic behavior of statistics which relate to the distance of vertices to the fringe: rank, height, and balance. I will focus on some general results on balanced trees using analytic techniques. Time permitting, I will also give a combinatorial proof of a recent result by Bona: the number of neighbors of leaves in increasing trees of size n is equal to the number of permutations of [n] with no fixed points. This talk is based on my doctoral thesis.