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Hopf algebras and Markov Chains
Algebra & Discrete Mathematics| Speaker: | Persi Diaconis, Stanford University |
| Location: | 1147 MSB |
| Start time: | Mon, Oct 29 2012, 4:10PM |
Description
Hopf algebras are gadgets invented and studied by
topologists and group theorists. In recent years, combinatorialists
have found them useful in keeping track of putting together and
tearing apart their natural objects. In joint work with Amy Pang and
Arun Ram we have found that we can associate a Markov chain with
combinatorial Hopf algebras. These specialize to riffle shuffling and
Kolomogorov's model of rock breaking (among many others). The Hopf
machine gives all the eigenvalues and eigenvectors.