(joint with asif shakeel, jiri lebl & david meyer)

the content of my previous ''fun with gerbes" talk (of which the
current talk is wholly independent) was etale homotopy 2-types via
grothendieck's theory of champs (the translation stack is awful), and the
content of this talk will be applications to lefshetz theorems. a
particular feature of having the right definition of higher homotopy
groups via n-categories is that the lefschetz theorem becomes a more or
less tautological induction, and at the very least i'll explain the
initial $\pi_0$ step in the induction- typically all problems in this area
are, when correctly understood, are problems about $\pi_0$. a manuscript
containingi the material from the "fun with gerbes" series is available
here: http://arxiv.org/abs/1507.00797