I will describe some joint work with Todorcevic on the Tukey theory of ultrafilters on the natural numbers. The notion of Tukey equivalence 
 tries to capture the idea that two directed posets "look cofinally the same", or have the same "cofinal type". As such, it provides a device 
 for a rough classification of directed sets based upon their "cofinal type", as opposed to an exact classification based on their isomorphism 
 type. This notion has recently received a lot of attention in various contexts in set theory. As background, I will illustrate the idea of rough 
 classification with several examples, and  explain how rough classification based on Tukey equivalence fits in with other work in set theory. The 
 talk will be based on the paper "Cofinal types of ultrafilters". A preprint of the paper is available on my website: http://www.math.toronto.edu/raghavan .