Abstract: What does it mean for an infinite binary sequence to be random? In this talk, I'll discuss three standard approaches that we can use to define randomness and show how to formalize them using recursion theory. After presenting some classical results in the area, I will show why a kind of randomness that Keng Meng Ng and I defined and studied satisfies one of our most basic intuitions. No knowledge of mathematical logic will be assumed.

This talk will be accessible to graduate students.