Seminari del Dipartimento di Matematica

Seminario del 2013

Prof. Gerardo Mendoza (Dept. of Math., Temple University)

Topological constraints of global hypoellipiticity

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

analisi matematica

Let M be a closed manifold, E, F be complex vector bundles over M, and P be a pseudodifferential operator mapping smooth sections of E to smooth sections of F. I will first discuss implications on the relation between E and F when P is elliptic, then implications on the relations between these vector bundles and M when E and F are line bundles, M a surface and P a first order globally hypoelliptic differential operator of principal type. At the end of the talk I will return to ellipticity and discuss some open problems. The talk is based on joint work with H.Jacobowitz (Indiana Univ. Math J., 2002 and TAMS, 2003) and with A.P.Bergamasco and S.L.Zani (Comm. PDE, 2012).