Quantum groups and Hopf algebras in combinatorics

Marcelo Aguiar – 22 February 2010

This talk will review the construction of quantum groups (deformations of simple Lie algebras) via quantum symmetric algebras, and explain how it can be extended by introducing a combinatorial structure in the form of a species, as defined by Joyal. This will lead us into the consideration of Hopf monoids in species, a notion that will be defined and for which examples will be given. Very little knowledge of any of the above notions will be assumed.