Mathematicians, as writers, are often lucky to avoid fixed deadlines for producing their works (or at least, it is my experience…). Exceptions arise, and I’ve been quite busy during the last few weeks in finishing to prepare the version of the lecture I gave at the Verbania Conference, which will appear in a special proceedings volume of the Milan Journal of Mathematics.

The deadline for this submission is on Monday (so I’m not late); if anyone has remarks, corrections, questions (“insulting or otherwise”, as I remember the chairman of an interesting AMS Session putting it, some time in 1998), there’s still one day for me to amend the text.

My main emphasis has been to try to present some of the theory and applications surrounding the Deligne Equidistribution Theorem, for non-specialists (in particular, for readers with little experience in algebraic geometry). So suggestions on how to improve the writing by “doing the right thing” (whether that means working on algebraic stacks, using derived categories, playing with perverse sheaves, making monodromy more Tannakian, or lots of other stuff I don’t really understand) will probably not be so useful…

In Proposition 3, f should be replaced by phi_j.

Thanks for the correction, that was a particularly bad typo.

I’ve put up an updated version, which also contains a sizable collection of corrections for typos pointed out by D. Zywina.