[PAST EVENT] Mathematics Colloquium: Andreea Nicoara (University of Pennsylvania)
February 16, 2015
2pm - 3pm
Abstract: The dbar equation is by far the most important partial differential equation in the field of several complex variables. When posed on a domain in C^n, the corresponding boundary value problem is called the dbar-Neumann problem. This problem, which turned out not to be elliptic, was solved in the 1960s by Joseph J. Kohn in the strongly pseudoconvex case and by Lars Hormander in the pseudoconvex case. The next line of inquiry was trying to gauge when the solution to the dbar-Neumann problem gained in differentiability with respect to the data, a property called subellipticity. In the late 1970s, Joseph J. Kohn proposed a new approach involving subelliptic multipliers. Much to his and everybody else's surprise, these subelliptic multipliers have amazing algebraic properties. I shall describe my work on subelliptic multipliers and the progress I have made on the central open problem called the Kohn Conjecture.