THE SEMINAR

THEORY OF DUALITY

DEPARTMENT OF MATHEMATICAL METHODS IN PHYSICS



On the 19th of January 2017, at 10:15 a.m.

Jan Dereziński (KMMF WFUW)

will give a talk on

"Almost homogeneous Schrödinger operators"

Abstract
First, I will describe a certain natural holomorphic family of closed operators with interesting spectral properties. These operators can be fully analyzed using just trigonometric functions.

Then, I will discuss 1-dimensional Schrödinger operators with a x-2 potential with general boundary conditions, which I studied recently with S. Richard. Even though their description involves Bessel and Gamma functions, they turn out to be equivalent to the previous family.

Some operators that I will describe are homogeneous — they get multiplied by a constant after a change of the scale. In general, their homogeneity is weakly broken — scaling induces a simple but nontrivial flow in the parameter space. One can say (with some exaggeration) that they can be viewed as "toy models of the renormalization group".

The seminar takes place on Thursdays from 10:15 a.m. to 12:00 in the room 2.23 of the main building of the Faculty of Physics (the 2nd floor), Pasteur Str. 5, Warszawa.
Additional information can be found on the webpage http://oldwww.fuw.edu.pl/KMMF/sem.czw.przedp.html.