Mathematics Colloquium
Speaker: Saikat Mazumdar, IIT Bombay
Title: Conformal Powers of the Laplacian, Q-Curvature, and the Compactness Problem
Time, day and date: 4:00:00 PM - 5:00:00 PM, Wednesday, October 15
Venue: Ramanujan Hall
Abstract: The conformal powers of the Laplacian, known as the GJMS operators, are a family of conformally invariant differential operators with leading term a power of the Laplacian, and the Q-curvature is the associated scalar invariant. They arise naturally and provide a unifying framework connecting important developments in geometry, analysis, and mathematical physics.
In this talk, I will consider the question of compactness of constantQ-curvature metrics on a closed Riemannian manifold. This is the higher-order analogue of the compactness problem for conformal metrics with constant scalar curvature. I will outline the background, motivations, and key challenges, and present some of my results in this direction. This is a recent work with Bruno Premoselli (ULB Brussels).