Counting maximal lattices.

n this talk, I will give a “good” lower and upper bounds
for the number of maximal irreducible lattices in a semisimple Lie
group over a positive characteristic local field, e.g. SL(n,F_q
((t))).

This should serve as a first step toward counting all
irreducible congruence subgroups. Such a result can be viewed as a
quantitative version of Wang’s theorem. I should also say that
recently the characteristic zero case have been handled by M.
Belolipetsky and A. Lubotzky.