Polynomial functors -- from elementary arithmetic to infinity-operads

In their simplest form, polynomial functors are endofunctors of the
category of sets built from sums and products. At first they can be
considered a categorification of the notion of polynomial function, but it
has turned out the theory of polynomial functors is more generally an
efficient toolbox for dealing with induction, nesting, and substitution.
The talk will highlight some of these aspects in combinatorics, logic, and
homotopy theory.