Jean-Claude Cuenin (Loughborough University)

Spectral Geometry Seminar

Title: Schrödinger operators with complex potentials: Beyond the Laptev-Safronov conjecture.

Abstract: I will report on recent progress concerning eigenvalues of Schr¨odinger operators with complex potentials. This talk can be seen as a continuation of the recent talk by Sabine B¨ogli (Durham) in the same seminar series, where a counterexample to the Laptev-Safronov conjecture was presented. I will explain how techniques from harmonic analysis, particularly those related to Fourier restriction theory, can be used to prove upper and lower bounds. Then I will present new results that show that in some cases one can go beyond the threshold of the counterexample.

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