Seminario di Equazioni Differenziali e Applicazioni: “On the Dirac equation in dispersive PDEs”

Venerdì 19 Maggio 2017, ore 10:00 - Aula 2BC30 - Federico Cacciafesta


Venerdì 19 Maggio 2017 alle ore 10:00 in Aula 2BC30, Federico Cacciafesta (Università di Padova) terrà un seminario dal titolo “On the Dirac equation in dispersive PDEs”.

The Dirac equation is one of the most important equations in quantum mechanics, and is widely used in several applications. In this talk, after introducing the main tools and giving a brief overview on the general topic, I will present some recent results obtained on the dynamics of the perturbed Dirac equation, as well as some open problems and projects that I am currently working on. In particular, I will focus on dispersive estimates for the Dirac-Coulomb model and related problems (such as the study of well-posedness for a nonlinear Dirac field interacting with a point nuclear dynamics and, in general, the study of dispersive PDEs with critical potentials) and for the Dirac equation on a non flat background. The purpose of the talk will be to show how many strategies that “easily” give strong results for the Schroedinger equation become very complicated when transposed to the Dirac setting: this is mainly due to the rich algebraic structure of the Dirac operator, and this is the reason why several relatively elementary questions still need to be answered.

Rif. Int. M. Bardi, P. Mannucci, C. Marchi

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