Seminarium KMMF "Teoria Dwoistości"

I will report on recent progress concerning eigenvalues of Schrödinger operators with complex potentials. In the first part of the talk I will explain how techniques from harmonic analysis (related to Fourier restriction theory) can be used in the context of spectral theory of Schrödinger operators. I will give some details on the recent counterexample to the Laptev-Safronov conjecture.In the second part of the talk I will try to convince you that the counterexample is non-generic. More precisely, I will show how the decay assumptions can be weakened under randomization. The tools used (multilinear expansion of the Born series, discretization and localization, entropy bounds, epsilon removal) may be of independent interest. To attend our online seminar, please use the Zoom identificator: https://us02web.zoom.us/j/8145917621?pwd=bVVKend0SHFKNUNyUUQ4cWNRK3laZz09