Complex Geometry seminar - Carlo Scarpa, Monday 14.04

[Jacopo Stoppa]

On Monday, 14.04 at 10:00 in room 136 (SISSA), Carlo Scarpa (Université Lyon 1) will give a seminar in the Complex Geometry series.

Title: The CR Yamabe invariant and constant scalar curvature Kähler metrics
Abstract: One of the most studied problems in Differential Geometry is the existence of metrics with constant scalar curvature. In the 1980s, the celebrated solution of the Yamabe problem by Trudinger, Aubin, and Schoen established that on a closed manifold one can always find a constant scalar curvature metric, in each conformal class of Riemannian metrics. In the context of Kähler geometry however the problem is still largely open. In this talk, I will present some progress in an ongoing project with Abdellah Lahdili (Université du Québec à Montréal) and Eveline Legendre (Université Lyon 1), in which we propose an approach to the existence of constant scalar curvature Kähler metrics that uses tools first appearing in the solution of the Yamabe problem in CR geometry. In particular, I will explain how one can use the CR Yamabe invariant to detect the existence of constant scalar curvature Kähler metrics.

Best,
Jacopo