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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

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.