Tommaso Pacini, University of Torino
Kahler techniques beyond Kahler geometry: the case of pluripotential theory
Classical pluripotential theory was introduced into complex analysis in the 1940's, as an analogue of the theory of convex functions. In the early 2000's, Harvey and Lawson showed that both pluripotential theory and many of its analytic applications make sense in a much broader setting.
Starting with the work of Calabi in the 1950's, however, it has become clear that pluripotential theory is central also to Kahler geometry. In particular, it is closely related to the cohomology of Kahler manifolds via Hodge theory and the ddbar lemma, and it provides one of the main ingredients in proving the existence of canonical metrics.
Work in progress, joint with A. Raffero, shows how parts of this "second life" of pluripotential theory extend to other geometries, hinting towards new research directions in the field of calibrated geometry and manifolds with special holonomy.
The goal of this talk will be to present a non-technical overview of some of these topics, aimed at non-specialists.
MC 5501