Lars Brink and SIC_POVMs

Abstract

The notion of SIC-POVMs comes from quantum information theory, and they were not on the horizon when I was Lars Brink's student in the early 80s. In the summer of 2022 I told Lars that I know how to use number theoretical insights to construct SIC-POVMs in any Hilbert space of dimension $n^2+3$, and that the construction provides a geometric setting for some deep number theoretical conjectures. I will give a sketch of this development, of what it was like to be Lars' student, and of what his reaction to our construction was.