Groups with polynomial geodesic growth

Classic growth functions count number of elements at a given distance from the identity. Geodesic growth counts the number of geodesics of a given length, allowing for more than one geodesic per element. In this talk we will study which groups can have polynomial geodesic growth function, will prove some results, and will conjecture which ones are exactly these groups. This is joint work with Martin Bridson, Murray Elder and Zoran Sunic.