Geometric Analysis in Phase-Space and PDEs

Areas: Analysis

Research activities of the group:

  • Analytic hypoellipticity of sums of squares of vector fields;
  • Local and global solvability of degenerale operators and operators with multiple characteristics;
  • Almost-positivity a priori estimates (Fefferman-Phong, Melin, Hörmander) for pseudodifferential and systems of pseudodifferential operators on Rn and on Lie groups;
  • Cauchy problem for weakly hyperbolic operators in presence of transitions of the geometry of bicharacteristics;
  • Well-posedness of the Cauchy problem for operators with real characteristics;
  • Well-posedness of first-order Hamilton-Jacobi equations and propagation of singularities along generalized characteristics;
  • Well-posedness, smoothing properties and Strichartz estimates for dispersive equation.

Faculty:

Paolo Albano

Full Professor

Massimo Cicognani

Full Professor

Serena Federico

Junior assistant professor (fixed-term)

Marco Mughetti

Associate Professor

Alberto Parmeggiani

Full Professor

Research fellows - Ph.D. Students

Marcello Malagutti

PhD Student

Teaching tutor

External Collaborators:

Piermarco Cannarsa, Michael Reissig, Wei-Xi Li, Antonio Bove, Gerardo Mendoza, Gigliola Staffilani, Carlo Sinestrari, Michael Ruzhansky, Sandro Coriasco, Karel Pravda-Starov.