Some of the most classical problems in number theory concern counting primitive vectors inside increasing subsets of R^n.
Primitive lattices are the higher dimensional analog of primitive vectors, and therefore many counting and equidistribution problems regarding primitive vectors can be generalized to primitive lattices.
The topic of the talk is counding and equidistribution of primitive lattices, as well as its application to the distribution of free rational points on the Grassmannian.
The talk is based on joint works with Yakov Karasik, and with Tim Browning and Florian Wilsch.