Recently several fundamental works have been done in Geometry of numbers. Beside Bhargava's revolutionary ideas (an of course the contribution of his students), Ergodic theory is a new idea that plays an important role in Modern Geometry of Numbers. It seems to me that several ideas are coming from Margulis and E. Lindenstrauss. 

Here are a list of works in this area which I think they are extremely interesting

1. [Minkowski's theorem for random lattices][1], Margulis 


2. [Logarithm laws for unipotent flows][2]. I, Athreya; Margulis

3. [On the probability of a random lattice avoiding a large convex set][3], Strömbergsson 

4. [A note on sphere packings in high dimension][4], Venkatesh

5. [On the distribution of angles between the $N$ shortest vectors in a random lattice][5], Södergren, Anders

6. [Remarks on Euclidean Minima][6], Uri Shapira, Zhiren Wang

7. [On the Mordell-Gruber spectrum][7], Uri Shapira, Barak Weiss

8. [A solution to a problem of Cassels and Diophantine properties of cubic numbers][8], Uri Shapira


  [1]: http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&r=1&review_format=html&s4=&s5=Minkowski%2527s%2520theorem%2520for%2520random%2520lattices&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq
  [2]: http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&review_format=html&s4=Margulis&s5=&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=8&mx-pid=2538473
  [3]: http://www.ams.org/mathscinet/search/publdoc.html?amp=&loc=refcit&refcit=2538473&vfpref=html&r=1&mx-pid=2861748
  [4]: http://math.stanford.edu/~akshay/research/sp.pdf
  [5]: http://www.ams.org/mathscinet/search/publdoc.html?pg1=INDI&pg6=PC&s1=931224&s6=11&vfpref=html&r=1&mx-pid=2855800
  [6]: http://www.technion.ac.il/~ushapira/Papers/EuclideanMin.pdf
  [7]: http://www.technion.ac.il/~ushapira/Papers/gruber6.pdf
  [8]: http://www.technion.ac.il/~ushapira/Papers/GDP5.pdf