Abstract:
When numbers are added in the usual way, carries occur. It is natural to ask for typical numbers how many carries there are there and how they are distributed. It turns out that they form a Markov chain with an amazing transition matrix. This same matrix turns up in the analysis of the usual method of shuffling cards (seven shuffles suffice), in taking sections of generating functions, and elsewhere. I will explain all this in "English." The results show that interesting math can be found anywhere and that this math can illuminate even humdrum problems like adding numbers and shuffling cards.

Bio:
Persi Diaconis is a mathematician and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University and is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards. He received a MacArthur Fellowship in 1982.