We Took Things a Day at a Time
Copyright© 2017 by Rolf
Prologue
We met for the entrance ceremony for the same major. The Courant Institute is responsible for New York University’s undergraduate programs in computer science and mathematics. For some reason we sat together and talked on and off.
When everything was over, we continued to sit and talk. She said; I am taking special interest in Gitta Kutyniok courses on Harmonic Analysis and Signal Processing Seminar jointly with the Numerical Analysis and Scientific Computing especially the first one on Anisotropic Multiscale Systems on Bounded Domains.
“I nodded my head and said, “Ugh, uh huh”.
It must have given her enough time to catch her breath because she continued.
“Many important problems are governed by anisotropic features such as singularities concentrated on lower dimensional embedded manifolds, for instance, edges in images or shear layers in solutions of transport dominated equations. While the ability to reliably capture and sparsely represent anisotropic structures is obviously the more important the higher the number of spatial variables is, principal difficulties arise already in two spatial dimensions. Since it was shown that the well-known (isotropic) wavelet systems are not capable of efficiently approximating such anisotropic features, the need arose to introduce appropriate anisotropic representation systems. I think I can really sink my teeth into that, how about you?”
“There is a lot there and I agree your course should be a good one but for me when I saw they were offering Universality and hyperuniformity of Weyl-Heisenberg ensembles I’m going for that first.”
I continued. “The guy they have teaching it is from ARI in Vienna. This class outline says the Weyl-Heisenberg ensemble is a functional dependent class of planar determinantal point process (DPPs) associated with the Schrodinger representation of the Heisenberg group. (You all know what the Heisenburg Principle is, right. Schrodinger is the mouse in the box) He thinks other DPPs, for most choices of the function g, has no access to explicit formulas for the correlation kernel. To overcome this obstruction, he developed a new methodology based on phase space and operator theoretical principles.”
They looked at each other and started laughing. “You don’t know what I just said, do you?”
“Nope but I think I’m in love. Hi. I’m Shawn O’Donnell.”
“Hi Shawn O’Donnell, I’m Georgina Barnes, nice to meet you.”
Way in the back sat a row of teachers. As they were the only students around they garnered everyone’s attention as they walked out. The comments raised were all like, “Wow, were did they come from and can I get a dozen more like them?”
