The unifying theme of the research project is the analysis of partial differential equations ruling relevant classical or quantum models in domains where spatial singularities can be present. Singularities can develop as a consequence of the dynamics (blow-up), or they can be present from the beginning in the domain where the model is set. In this second case singularities can describe spatial inhomogeneities of the propagation medium (described for example by point or delta interactions with various co-dimension or by quantum graphs) or they can serve as effective approximations (zero range models). The plan of the project includes the following main research lines:

1. Systems of quantum particles with zero-range interactions

2. The semiclassical limit in presence of singular interactions

3. Schrödinger operators and singular interactions in acoustics: scattering theory

4. Nonlinear Schrödinger equation in domains with spatial singularities: stability, instability and asymptotic properties

Structure & People

Unit 1. University of Milano-Bicocca (Milan)

• Diego Noja - PI (University of Milano Bicocca)

• Andrea Sacchetti (University of Modena and Reggio Emilia)

• Federica Muscolino (University of Milano Bicocca)

Unit 2. University of Insubria (Como)

• Andrea Posilicano - Local Coordinator (University of Insubria)

• Claudio Cacciapuoti (University of Insubria)

• Hamidreza Saberbaghi (University of Insubria) 

Unit 3 Sapienza University of Rome 

• Alessandro Teta - Local Coordinator (Sapienza University)

• Domenico Finco (Uninettuno)