Shuffling Cards and Adding Numbers

When several large integers are added in the usual way 'carries' occur along the way. It is natural to ask: 'About how many carries are there and how are they distributed for typical numbers?' It turns out that these questions are intimately related to the mathematics of the usual way we shuffle cards. I will explain the mathematics of 'carries' (they are cocycles!), shuffling and the connection. This is joint work with Jason Fulman.