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.
This video was produced by Newcastle University, Australia, as part of the Symmetries in Newcastle seminar series.
