Koji Fujiwara

The rates of growth in hyperbolic groups

The growth rate of a finitely generated group is a fundamental object in the study of groups. It is also very much related to geometry. For example, Milnor proved in the 60s that if a compact manifold has negative sectional curvature, then its fundamental group has exponential growth. I will discuss the structure of the set of growth rates of a hyperbolic group, which is a finitely generated group of "negative curvature".