Alberto Parmeggiani

Full Professor

Department of Mathematics

Academic discipline: MATH-03/A Mathematical Analysis

Research

Keywords: Geometric analysis of PDEs Solvability Lower-bound estimates Spectral theory

Geometric analysis of PDEs, and in particular the almost-positivity of systems of pseudodifferential operators and the symplectic sub-unit geometry.
Geometric analysis of PDEs on compact Lie groups.
Solvability of PDEs, in particular that of systems of PDEs.
Spectral theory, and in particular the spectra (and pseudo-spectra) of polynomial-coefficient differential systems and the study of spectral zeta-functions of elliptic differential systems.
Hypoellipticity.
Well-posedness of the Cauchy problem for weakly hyperbolic operators.
Problems related to the weak KAM theory.