BCAM Scientific Seminar | Uncertainty principles and sharp stability results

We present some useful functional inequalities in spectral theory of differential operators, in the study of partial dierential equations or the stability of physical systems (motivated by quantum mechanics). We focus on two fundamental uncertainty principles (Heisenberg-Pauli-Weyl principle and Hydrogen principle). Mathematically, they are part of the wide class of inequalities of the Caarelli-Kohn-Nirenberg type that we apply to either scalar or vector elds. Best constants and extremizers are obtained. In addition, we show sharp stability results in L2 for such functional inequalities.

This talk is based mainly on joint works with Joshua Flynn (MIT, USA, email: jlynn@mit.edu), Nguyen Lam (Memorial University of Newfound-land, Canada, email: nlam@grenfell.mun.ca) and Guozhen Lu (University of Connecticut, USA, email: guozhen.lu@uconn.edu)