turkmath.org

The growth function of a finitely generated group measures how fast the balls in its Cayley graphs grow. This asymptotic invariant attracted a lot of attention starting from Milnor's questions and Gromov's theorem about groups which have polynomial growth. This talk will be a survey of history, open problems and recent developments around this notion. The main focus will be on groups whose growth is intermediate between polynomial and exponential. We will outline results related to generic growth in a family of groups of intermediate growth constructed by R. Grigorchuk.