Date & Time: Monday, February 1, 2010, 15:30-16:30
Venue: Ramanujan Hall
Title: Hopf Algebras in Topology, Combinatorics, and Representation Theory
Speaker: Marcelo Aguiar, University of Texas A & M
Abstract: Hopf algebras are prominent in various areas of mathematics. In algebraic topology, where the notion originated, they arise from topological groups or H-spaces. In combinatorics, they encode natural operations one may perform on a given type of discrete structure. In representation theory, they arise as deformations of simple Lie algebras (quantum groups).
This talk will describe a theory developed jointly with Mahajan that allows us to view the above constructions in a unified manner. It involves notions such as quantum symmetric algebras, bilax monoidal functors and Joyal's species. Very little knowledge of any of the above notions will be assumed.