What is... an operad?

Calista Bernard will explain what an operad is.

Abstract: Suppose we have a space with a multiplication that is not strictly associative, so $(xy)z$ and $x(yz)$ are not equal. If we want to multiply $n$ elements together, we now have many ways to do so depending on where we choose to put our parentheses. Often we have some additional data, such as paths between $(xy)z$ and $x(yz)$ and some coherency between these paths, and we would like to keep track of this data to see how to relate the different ways of multiplying $n$ elements. Operads provide a concise way of encoding this type of data of operations and relations between them. In this talk I will define operads and give examples that determine to what extent a multiplication is associative or commutative up to homotopy. In particular, I will discuss $E_n$-operads and their relationship to $n$-fold loop spaces.

"What is...?" is an accessible and non-technical seminar where speakers explain in one (short) lecture some object or theorem that they think is interesting. There will be drinks and snacks during the talk. See the seminar website for more information.