Event description
Abstract: In this seminar, we will give an overview of some recent results in non-Kähler geometry. In the first part, we will discuss the role of geometric flows in the study of Hermitian metrics and present results on the long-time behavior of the positive Hermitian curvature flow on a class of nilpotent Lie groups.
In the second part, we will discuss a joint work with L. Rubini and A. Tomassini on the existence of special Hermitian metrics under small deformations of the complex structure. Whereas the first part concerns the evolution of a Hermitian metric on a fixed complex manifold, here we vary the complex structure on a fixed differentiable manifold and investigate whether the existence of special Hermitian metrics is preserved.
The final part will focus on the algebraic and cohomological constraints imposed by the existence of astheno-Kähler metrics on nilmanifolds. We will also discuss the existence of geometrically Bott-Chern formal metrics on nilmanifolds and their relations with other special Hermitian metrics.
This first seminar will be largely non-technical, emphasizing the motivations, guiding questions, and problems that shaped my research during my PhD. The second seminar will be devoted to the final part of this talk, providing a detailed account of the techniques used in the proofs.
This is joint work in progress with Elia Fusi and James Stanfield.