Event description
Geometry of the Levi core
The Levi core of the boundary of a pseudoconvex domain was introduced by G. Dall'Ara and myself in relation to the Diederich-Fornaess index; it generalizes the idea of weakly regular stratification introduced by Diederic-Fornaess and later widely used by Catlin.
It turns out that the Levi core has connections with exact regularity (via D-F index) and compactness (via P_q property) of the "de bar"-Neumann problem.
The Levi core is non trivial when the boundary contains an analytic disc or, more generally, a local maximum set; the converse is an open problem.
I will sketch the construction of the Levi core and its links with the "de bar"-Neumann problem; if time allows, I will outline some attempts at finding some complex analytic structure inside the Levi core, under some additional hypothesis.