Abstract:In this seminar I will present some of my research activities related to the rigorous analysis of a quantum particle confined in a bounded region of space. In the first part of the seminar I ...
Abstract: In this talk I will present, in a very general way, some of my most recent works. I will show examples of how to use conformal geometry to prove some properties, including uniqueness, ...
Abstract: Let C be a Riemann surface, x_1,...,x_n a set of points on C, and a_1,...,a_n integers adding up to 0. The theorem of Abel and Jacobi determines when C carries a meromorphic function wi...
Abstract: Quantum systems with short-range interactions at sufficiently low energy are characterized by a wavelength so large that the fine details of the interactions become irrelevant and most ...
Abstract: For a uniform magnetic field, we provide a decomposition of operators commuting with the associated magnetic translations. As an application, we rewrite the energy per unit surface for an el...
Abstract: I will discuss the existence of turbulent solutions to a quantum hydrodynamic (QHD) system, with periodic boundary conditions. A suitable nonlinear change of variables (the Madelung transfor...
Abstract: Secondo la filosofia della congettura di Green-Griffiths-Lang, ci si aspetta che l'esistenza e la distribuzione dei punti razionali per le varietà che sono uniformemente non-iperboliche...
Abstract: Metastability phenomena show up in the dynamical behavior of a large variety of complex real world systems. From a mathematical point of view the dynamics of such systems may be modeled by m...
