Noncompact Hermitian symmetric spaces and homogeneous complex hypersurfaces

"Noncompact Hermitian symmetric spaces and homogeneous complex hypersurfaces", organizado polo CITMAga. Será impartido por Ivan Solonenko (Universität Stuttgart, Alemaña).

Data: Xoves 2 de maio de 2024.

Hora: 17:00 h.

Lugar: Aula 10 da Facultade de Matemáticas, USC.

Abstract:

In this talk, I will present some new structure theory for Hermitian symmetric spaces of noncompact type and give a detailed description of how the complex structure of such a space behaves with respect to the restricted root space decomposition of its isometry Lie algebra. Building on that, I will then present a partial classification result for homogeneous complex hypersurfaces (HCHs) in such spaces: we will discuss a complete classification of homogeneous cohomogeneity-two foliations with a complex leaf, as well as of cohomogeneity-one actions with a complex hypersurface as a singular orbit. In particular, we will see that every noncompact Hermitian symmetric space admits an HCH. Time permitting, I will demonstrate how this contrasts (starkly) with the compact type picture (where a full classification of HCHs is known).