Recently several fundamental works have been done in the area of the geometry of numbers. Beside Bhargava's revolutionary ideas, and of course the contribution of his students, Ergodic theory is a new idea that plays an important role in modern geometry of numbers which seems to me that several ideas are coming from Margulis and E. Lindenstrauss's works.
Here is a list of papers in this area which I think are extremely interesting and important.
Minkowski's theorem for random lattices. Margulis (Russian) Problemy Peredachi Informatsii 47 (2011), no. 4, 104--108; translation in Probl. Inf. Transm. 47 (2011), no. 4, 398–402
Logarithm laws for unipotent flows. I, Athreya; Margulis
On the probability of a random lattice avoiding a large convex set, Strömbergsson
A note on sphere packings in high dimension, Venkatesh
On the distribution of angles between the $N$ shortest vectors in a random lattice, Södergren, Anders
Remarks on Euclidean Minima, Uri Shapira, Zhiren Wang
On the Mordell-Gruber spectrum, Uri Shapira, Barak Weiss
A solution to a problem of Cassels and Diophantine properties of cubic numbers, Uri Shapira