The strong HRT conjecture asserts that the time-frequency translates of any nontrivial function in L^2(R) are linearly independent. The weak HRT conjecture has the same formulation, but this time for Schwartz functions. Prior to our work, the only result of a reasonably general nature was Linnell's proof in the case when the translates belong to a lattice. I will briefly describe an alternative argument to Linnell's (joint work with Zubin Gautam), inspired by the theory of random Schrodinger operators. Then I will explore both some solo and joint work (with Alexandru Zaharescu) involving a number theoretical approach to the HRT conjecture, for some special 4 point configurations.