Felipe Leitner - About the Kohn‒Dirac operator on CR manifolds
Jurekfest - day 1, lecture 3.
Speaker: Felipe Leitner (introduction by Jurek Lewandowski).
Title: About the Kohn‒Dirac operator on CR manifolds
Abstract: CR geometry is a parabolic geometry, which naturally appears in complex analysis and is closely related to conformal geometry of spacetimes via the Fefferman construction. I will introduce in my talk spinor fields on CR manifolds and discuss a kind of Dirac equation. I present concrete computations and lower bounds for the spectrum of the Dirac operator. In the limiting case some kind of twistor equation arises. We solve some special cases of this overdetermined equation. Finally, I will discuss vanishing results for harmonic spinors and obstructions to positive Webster curvature. The vanishing is related to Kohn–Rossi cohomology groups.
Slides: http://jurekfest.fuw.edu.pl/slides/le...
Link to conference's webpage: http://jurekfest.fuw.edu.pl.