Infinity categories and infinity operads

I will discuss some aspects of the simplicial theory of

infinity-categories which originates with Boardman and Vogt, and has

recently been developed by Joyal, Lurie and others. The main purpose of

the talk will be to present an extension of this theory which covers

infinity-operads. It is based on a modification of the notion of

simplicial set, called 'dendroidal set'. One of the main results is that

the category of dendroidal sets carries a monoidal Quillen model

structure, in which the fibrant objects are precisely the infinity

operads,and which contains the Joyal model structure for

infinity-categories as a full subcategory.

(The lecture will be mainly based on joint work with Denis-Charles

Cisinski.)