martedì 7 ottobre, alle ore 14:00 in  aula SP1L

prof. Qi Guo, Renmin University, Pechino

Titolo: Relativistic and Discrete Eigenvalue Problems

Abstract: In this talk, I will present several distinct eigenvalue problems and explore their interconnections. The first problem concerns the existence of ground states for the nonlinear Dirac equation with power-type nonlinearities. I will demonstrate that, in the nonrelativistic limit, these Dirac ground states converge to the nonlinear Schrödinger ground state, thereby providing a rigorous foundation for certain physical principles. The second problem involves the eigenvalue problem of the discrete Laplacian on a newly introduced random graph model, which features a higher number of connected graphs. I will examine bounds for the first eigenvalue of the discrete Laplacian and discuss an application within hyperbolic geometry.