In this talk, we will discuss a further refinement of the restricted invertibility principle first put forward by Bourgain and Tzafriri. Namely, we will show that any full rank matrix has a large submatrix whose smallest singular value is of the same order as the harmonic average of all singular values. We will also investigate the relation to the problem of estimating the Banach-Mazur distance to the cube. Joint work with Assaf Naor.

https://sites.google.com/view/paw-seminar