December 13, 2021, 14:00 Sala Consiglio - VII Piano Politecnico di Milano Building 14 (Nave), Campus Leonardo P.zza da Vinci 32, Milano, Italy

SPEAKER: Riccardo Adami (Politecnico di Torino)

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

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 logaritmico 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.

**Important Notice:** To access the seminar room, please wait at the entrance of the Mathematics Department, Building 14. One of the organizers will let you in using the dedicated elevator for staff. As per internal regulations of Politecnico, the COVID19 green certificate will be checked before entering the room.