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. Margulis (Russian) Problemy Peredachi Informatsii 47 (2011), no. 4, 104--108; translation in Probl. Inf. Transm. 47 (2011), no. 4, 398–402

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

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

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

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

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

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

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

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.

1. 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

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

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

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

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

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

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

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

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, Margulis

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

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

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

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

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

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

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

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. Margulis (Russian) Problemy Peredachi Informatsii 47 (2011), no. 4, 104--108; translation in Probl. Inf. Transm. 47 (2011), no. 4, 398–402

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

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

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

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

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

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

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