Modul: MAT675 PDE and Mathematical Physics

## Ground states for the two-dimensional NLS in the presence of point interactions

Talk by Prof. Dr. Riccardo Adami

Speaker invited by: Prof. Dr. Benjamin Schlein

**Date:** 18.11.21 **Time:** 18.00 - 19.30 **Room:** Y27H35/36

We prove the existence of ground states, i.e. minimizers of the energy at fixed mass, for the focusing, subcritical Nonlinear Schroedinger equation in two dimensions, with a linear point interaction, or defect. Ground states turn out to be positive up to a phase, and to show a logarithmic singularity at the defect. The analogous problem has been widely treated in the one dimensional setting, including the case of graphs. The two dimensional version is more complicated because of the structure of the energy space, that is larger than the standard one. This result opens the way to the study of nonlinear hybrids. This is a joint work with Filippo Boni, Raffaele Carlone, and Lorenzo Tentarelli.