The beauty and mystery of total variation

The variational distance between probability distributions is, in some natural sense, the canonical one. Its central importance is readily evident in probability, statistics, privacy, and algorithms.
Unfortunately, it is an analytically unwieldy object, and in particular, is strongly computationally intractable, even for products of Bernoullis. This talk, after providing the necessary background, will discuss a series of approaches to obtaining analytically tractable estimates on the total variation distance between product distributions. Some elegant mathematical surprises are promised.