An Introduction to Species and Operads

This talk will be essentially expository. Its goal is to connect two different types of structure, species and operads, which are used in combinatorics and algebraic topology respectively, and hopefully generate discussion. We will first review the definition of species, in the sense of Joyal, and some of the ways they show up in combinatorics. We will then discuss operads, which are a special kind of species, and see how operads are related to trees and how they can be used to control algebraic structures (e.g. associative monoid structure, commutative monoid structure and braidings).