The general subject of this talk will be how we can make precise the notion of a random binary sequence. The focus will be on introducing one particularly successful notiuon of randomness (due to Martin-Lof) that draws on and intersects with concepts from computability theory. Multiple equivalent ways of getting at this notion will be explored, in order to see how it can be modified in various directions. Some computability-theoretic background will be provided as part of the talk.

This is the the first in a projected series of talks by Ed Dean and Jason Rute.