# Dendroidal sets, Cisinski-Moerdijk model structure, and first steps towards a geometric realization

*Algebra/Geometry/Topology Seminar*

*by Ittay Weiss*

*Institution:*University of the South Pacific

*Date: Fri 27th January 2012*

*Time: 3:15 PM*

*Location: 213 Richard Berry*

*Abstract*: Dendroidal sets were introduced in 2007 in the context of the homotopy theory of operads. From the beginning there were two obvious problems that needed to be addressed: homotopy theory and geometric realization. Very recently Cisinski and Moerdijk, in a series of three articles, settled the homotopy theory problem by means of suitable Quillen model structures. The problem of the geometric realization remains open. In the talk, assuming no prior knowledge of dendroidal sets or Quillen model structures, I will explain what dendroidal sets are and present the necessary ingredients needed for establishing the first of the model structures. If time permits I will explain precisely what the problem of the geometric realization is and hint at a few first steps for an answer.