CNRS & CEREMADE,
Université Paris Dauphine,
Place de Lattre de Tassigny,
F-75 016 PARIS.
Office: C 606,
Email: pizzichillo@ceremade.dauphine.fr.
I got my Bachelor degree and my Master degree in Mathematics at "University of Bari".
From October 2014 to December 2017 I have been a PhD student under the supervision of Prof. Luis Vega. In my thesis, I considered the delta-shell interaction on bounded and smooth domains and its approximation by the coupling of the free Dirac operator with shrinking short-range potentials, getting surprising results related to Klein's Paradox. Moreover, I investigated the Dirac operator perturbed by a particular class of Coulomb-type spherically symmetric potentials, describing the self-adjoint realisations of this operator in terms of the behaviour of the functions of the domain in the origin.
From December 2017 to October 2018 I have been a postdoc under the supervision of Prof. Luis Vega. During this period I worked on Hardy-type inequalities for the Dirac operator. We exploited these inequalities to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix valued potentials of Coulomb type: we characterised its eigenvalues in terms of the Birman-Schwinger principle, and we bounded its discrete spectrum from below, showing that the ground state energy is reached if and only if the potential verifies some rigidity conditions.
I am currently working as a Postdoctoral Fellow at CEREMADE - Université of Paris-Dauphine under the supervision of Prof. Mathieu Lewin.