Geometric properties of groups that are not geometric ... or are they?
Abstract: A property of a finitely generated group is said to be "geometric" if it is preserved under change of finite generating set. In this talk we consider two properties of a finitely generated group that are very geometric in flavor, but are dependent on the choice of (standard weighted) generating set. The properties are called "almost convexity" and the "falsification by fellow traveler property". We will discuss some of the many nice aspects of groups enjoying these properties, and then discuss how one might try to make them geometric.