Giuseppe Zampieri, professor of Mathematics at University of Padova since 1984 - Head of the nationwide PRIN research program "Microlocal Analysis" - Coordinator of the research unit "Algebaric and Complex Analysis" at University of Padua - Member of the scientific board of CIME foundation at Florence - Member of "Istituto Veneto di Scienze Lettere ed Arti" at Venice - Author of about one hundred publications in Algebraic Analysis and Complex Geometry

Research interests

Microlocal equations in real analytic and Gevrey category - Fundamental principle of Ehrenpreis - Theory of lacunas - Global existence of analytic solutions. This has been an active field of research since the 70's and early 80's which has attracted the interest of Garding, Hörmander, Bott, Sato, De Giorgi, Cattabriga to mention only a few. The new contribution consists in the geometric interpretation of the "Phragmén-Lindelöf principle" for existence of real analytic solutions in the formulation given by Hörmander. The geometry of the domain is completely described in terms of the propagation cones of the differential operator: bicharacteristic lines or light cones (for the cases of simple and multiple characteristics respectively). A further contribution consists in proving that the analytic solvability "propagates" to Gevrey indices s < m/(m - 1) where m is the multiplicity. Leaders in this line of research were Cattabriga, Andreotti, Kaneko.

Algebraic Analysis - Microlocal theory of boundary value problems - Light reflection. In this field merge the contribution of various theories such as the symplectic and differential geometry, the analytic theory of PDE's, the theory of sheaves and derived categories. Among the leading figures are Sato, Kashiwara, Leray, Schapira. The new contribution is the theory of the singular Lagrangians which are naturally associated to the manifolds with boundary. The theory of the second microlocalization at the boundary and the propagation of the singularity for the non-microcharacteristic equations has also been settled. There have been as coauthors in this research: Schapira, Kataoka, Tose, D'Agnolo.

Complex and CR Geometry - Analytic discs in complex spaces - Integral representation of the solutions to the tangential CR system - Uniform L^2 estimates - Kobayashi metric and extremal discs - Holomorphic extension from convex hypersurfaces - CR envelopes. The new contribution are a theory of analytic discs with singular boundary, the discs in symplectic spaces and their transformations, the precise description of the forced CR extension, the uniform estimates for weakly q- pseudoconvex domains of C^n. The techniques are various: Hölder and L^2 estimates, integral representation by a kernel, systems of real/complex vector fields, stationary/extremal discs. Some reference names are those of Henkin, Tumanov, Kohn, Nirenberg. There have been as coauthors: Tumanov, Zaitsev, Baracco, Ahn.

Direction of thesis: A. D'Agnolo, C. Marastoni, A. Scalari, A. Giacobbe, F. Tonin, L. Baracco, P.N. Bettiol, A. Siano, R. Mascolo, R. Marigo.