Week 10, Tuesday 18th March
Cong Chen Some combinatorial group theory
The word norm for any element of a group, given a symmetric generating set, is the length of the shortest representation of that element as a word in the generators. It may also be thought of as the graph norm on the Cayley graph. A quasimorphism from a group $G$ to a normed group (usually the Reals) is a map $f$ such that $d(f(x)f(y),f(xy))$ is absolutely bounded. I will discuss some folklore connecting these combinatorial and geometric ideas.