|Date: Friday, January 24, 2014
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Card Shuffling and other Hopf-Power Markov Chains
Abstract: The Hopf-power Markov chain is a new way to model the breaking and recombination of combinatorial objects. Its transition probabilities come from the coproduct-then-product operator on a combinatorial Hopf algebra, so it can be analysed using Hopf algebra structure theory. Key examples include the Gilbert-Shannon-Reeds model of riffle-shuffling of a deck of cards, a model of tree-pruning, and the restriction-then-induction of representations of the symmetric group. In this talk, I'll give the general definition of these processes, and explain how theorems such as Cartier-Milnor-Moore and Poincare-Birkhoff-Witt give information about their long term behaviour. This is a generalisation of joint work with Persi Diaconis and Arun Ram. No knowledge of Markov chains will be assumed.
Speaker: Amy Pang
Institution: Stanford U.