Abstract:

1. Are there infinitely many 2 x 2 integral matrices of determinant 2 all of whose elements are prime numbers ?
2. If so, how many such matrices one should expect to find in ball of radius T in the space of 2 x 2 matrices ?

We will explain an approach towards these questions, via sieve methods, non-Euclidean lattice point problems, and ergodic theorems on Lie groups. Based on joint work with Peter Sarnak.