The leaves of a tree: a dendroidal infinite loop space machine

Dendroidal sets and dendroidal spaces form a generalisation
of simplicial sets and bisimplicial sets, whose homotopy theory
models simplicial operads. These dendroidal objects are defined by
replacing the finite linear orders making up the simplicial category
by finite rooted trees.
Taking the leaves of a tree induces a functor from dendroidal
spaces to Segal's Gamma spaces whose homotopy theory models
connective spectra. I will explain that this functor induces a
Quillen equivalence between a homotopy theory for dendroidal sets
or spaces to the homotopy theory for special Gamma spaces. The
proof is based on a version of the Barratt-Priddy-Quillen Theorem
for such special (but not necessarily group-like) Gamma spaces.
The lecture is based on joint work with Pedro Boavida, and
hopefully clarifies earlier work of Heuts and Nikolaus-Basic.