(University of Michigan)
"Krull dimension for limit groups"
Abstract:Limit groups are the analog in algebraic geometry of the free group of coordinate rings of varieties, and play a central role in the study of sets defined over a free group. A basic fact in algebraic geometry is that varieties have finite Krull dimension, and the definition of dimension carries over naturally to the setting of free groups, raising the question of their finite dimensionality. I will discuss the basic features of limit groups, and give an overview of the proof that the varieties they correspond to are indeed finite dimensional.