**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.