Thursday, October 2, 2025 — 2:30 pm — aula M2.5, edificio Matematica
Relativistic and Discrete Eigenvalue Problems
Abstract: In this talk, I will present several distinct eigenvalue problems and explore their interconnections. The first 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. 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.