Emily Casey, University of Washington

PDL C-401

*This is the first talk in a two-talk series.*

*What is a rectifiable set?*We can think of a rectifiable set as the image of countably many "nice'' maps—in particular, maps that have nice differentiability properties. So, it would make sense that at almost every point of these

*rectifiable sets*there should be a tangent. But, is there? And if so, in what sense? We seek to understand these questions through the use of many pictures and examples. This talk is purely expository and is based on a survey:

*Rectifiability; A Survey*by Pertti Mattila. The second talk will be by Ignacio Tejeda, and seeks to understand rectifiable sets via their projections.