On Card Shuffling

I will talk about some famous results of Bayer and Diaconis (1992) which permit a rigorous answer to the following question: given a deck of n cards, how many times should it be shuffled so that the deck is in approximately random order? The goal is to prove the existence of a cutoff phenomenon: if the deck is shuffled less than (3/2)log(n) times it is 'far' from being random but after that it is 'very close' to being random. Aside from practical interest (in casinos and magic tricks) and from having made the front page of the New York Times, this leads to some really beautiful mathematical developments. The level of the talk will be as basic as possible.