The Sato-Tate conjecture is about the local data from elliptic curves
and how such data converges to a specific distribution, much like the
Central Limit Theorem. I'll talk about Sato-Tate and other conjectures
in which the data differentiates between elliptic curves rather than
finding commonalities. You won't need to know what an elliptic curve is
to understand Sato-Tate and other conjectures about them.