Polina Baron. Schrӧdinger operators and their spectral theory. June 1, 2021

Schrӧdinger operators are the operators of the form

[Hψ](x)=ψ(x+ρ)+ψ(x−ρ)+V(ρ)ψ(x),

where ρ is the period and V(ρ) is a function called the potential. They arise in many areas of mathematics, including quantum mechanics, field theory and quantum groups. Of particular interest is the spectral theory of Schrӧdinger operators, which has been in active development since around the 1970-s. We will discuss history, applications, and spectral theory of Schrӧdinger operators, with a special focus on the case of dynamically defined potentials, including the results that were a part of Artur Avila’s Fields Medal in 2014.

Видео Polina Baron. Schrӧdinger operators and their spectral theory. June 1, 2021 канала Mathematics at HSE