Title: PDEs, Spencer cohomology and existence of analytic solutions
Abstract: If you're on the mailing list of this seminar, you probably took a course on partial differential equations at some point during your studies. And in that course, or maybe in some other way, you probably have seen a "power series" approach to finding solutions to PDEs. In this talk I will talk about power series solutions to PDEs, and highlight how they reveal some interesting structure. I will introduce the formalism of PDEs, and introduce the Spencer cohomology as the obstruction to solving your power series one degree further. If all of the Spencer cohomology groups vanish, then the system is in involution and your PDE is at least formally solvable. However, to show convergence of those power series, one needs homotopy operators for the Spencer complex whose norms satisfy certain estimates, and I will talk about this too.
