Infinity-operads as polynomial monads

Lurie's infinity-operads are defined as certain Gamma-spaces, in
the spirit of May-Thomason.  A different approach to infinity-
operads is due to Cisinski and Moerdijk in terms of dendroidal
Segal spaces.  After outlining these approaches, I will explain
a new model for infinity-operads, given in terms of polynomial
monads.  This provides an infinity version of the classical
viewpoint that operads are monoids in the monoidal category of
species/analytic functors under the substitution product.
Leaving out the technical details, I will explain the ideas
behind the proof that the infinity-category of analytic monads
is equivalent to the infinity-category of dendroidal Segal
spaces.  This is joint work with David Gepner and Rune Haugseng.