Seminarium Fizyki Materii Skondensowanej

I will discuss the theory of Schr\"odinger operators with 1/x^2 potentials.This is a class of objects with surprisingly rich mathematical phenomenology, which should be close to physicists' hearts: the "running coupling constant" flows under the action of the "renormalization group", there are two "phase transitions", attractive and repulsive fixed points, limit cycles, breakdown of conformal symmetry, etc. I will discuss both the self-adjoint and non-self-adjoint cases. The latter have quite curious properties and I am looking for their physical applications.