I will discuss the following counting problems: (1) the number of solutions of certain
restricted linear congruences in several variables, connected to Ramanujan sums, (2) the
number of $r$-tuples of positive integers with $k$-wise relatively prime components,
(3) the average number of subgroups of rank two and rank three abelian groups.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/246