An Invitation to Hypoelliptic Operators and H憿孑ander's Vector Fields

?Hormander's operators are an important class of linear elliptic-parabolic degenerate partial differential operators with smooth coefficients: this text provides the reader with a general overview of the field, with its motivations and problems, some of its fundamental results, and some recent lines of development. These topics have been intensively studied since the late 1960s and are still an active field of research.

Prof. Marco Bramanti Associate Professor of Mathematical Analysis Department of Mathematics School of Information Engineering - Politecnico di Milano (Italy) - Graduated in Mathematics in 1987 at the University of Milano (Italy), under the guide of Prof. Sandro Salsa.- Researcher in Mathematica Analysis since 1990 at the Polytechnic of Milano (Italy).- Ph.D. in Mathematics in 1993 (University of Milano), under the guide of Prof. Sandro Salsa. - Associate Professor in Mathematica Analysis since November 1998 at the University of Cagliari (Italy), since November 2001 at the Polytechnic of Milano (Italy). He has been visiting professor at the University of Minnesota (1993), he had a fellowship from the Italian "Istituto Nazionale di Alta Matematica" (National Institute of High Mathematics), at the University of Florence (1988), he had taken part to the summer schools organized by the "Scuola Matematica Interuniversitaria" (Inter-university Mathematical School) at Perugia (1987) and Cortona (1990) and to many other courses, congresses and seminars. He has held conferences and communications in national and international scientific congresses.