On Yau’s uniformisation conjecture.
Organizers
Speaker
Ved Datar
Time
Tuesday, January 20, 2026 8:00 PM - 9:30 PM
Venue
Online
Online
Zoom 928 682 9093
(BIMSA)
Abstract
Yau’s uniformisation conjecture states that a complete non-compact n-dimensional Kahler manifold with positive bi-sectional curvature is bi-holomorphic to C^n. I will report on some recent progress (joint with Vamsi Pingali and Harish Seshadri) on this conjecture for Kahler surfaces with positive sectional curvature. In particular we prove that the square of the Ricci form is integrable on such manifolds, answering another question of Yau in the affirmative. Our new idea is to construct appropriate weights with finite Monge-Ampere masses, by solving complex Monge-Ampere equations.