Lieb-Thirring inequalities and other functional inequalities for orthonormal systems

Abstract

We review recent results on functional inequalities for systems of orthonormal functions. The key finding is that for various operators the orthonormality leads to a gain over a simple application of the triangle inequality. The operators under consideration are either related to Sobolev type inequalities or to Fourier restriction type inequalities.

18 pages; submitted to the proceedings of ICM 2022