Geometry and Complexity of positive cones in groups.

Abstract: A positive cone on a group $G$ is a subsemigroup $P$, such that $G$ is the disjoint union of $P$, $P^{-1}$ and the trivial element. Positive cones codify naturally $G$-left-invariant total orders on $G$. When $G$ is a finitely generated group, we will discuss whether or not a positive cone can be described by a regular language over the generators and how the ambient geometry of $G$ influences the geometry of a positive cone.

This will be based on joint works with Juan Alonso, Joaquin Brum, Cristobal Rivas and Hang Lu Su.

group theory

Audience: researchers in the discipline

Symmetry in Newcastle