Speaker: Pallavi Dani
Title: Filling Invariants for Groups
Affiliation: University of Oklahoma
Date: Thursday, January 31, 2008
Place and Time: Room 102, Love Building, 3:35-4:30 pm

Abstract. For any loop in a simply-connected Riemannian manifold, one can look for a disk of minimal area whose boundary is that loop. More generally, one can consider fillings of n-spheres by (n+1)-balls. These notions have natural analogues in the realm of finitely presented groups, where one models the group using suitably defined geometric spaces. I will discuss Dehn functions of groups, which capture the difficulty of filling spheres with balls. A fundamental question in the area is that of determining which functions arise as Dehn functions of groups. I will give an overview of known results and describe recent progress in the 2-dimensional case. This is joint work with Josh Barnard and Noel Brady.