ALE Ricci-flat 4-manifolds and harmonic forms
Organizers
Speaker
Hao Yan
Time
Monday, December 9, 2024 3:30 PM - 5:00 PM
Venue
A3-2-301
Online
Zoom 559 700 6085
(BIMSA)
Abstract
This talk focuses on the study of Asymptotically Locally Euclidean (ALE) Ricci-flat 4-manifolds, a class of Riemannian manifolds significant in geometric analysis and mathematical physics. Starting with a review of foundational concepts such as the Ricci-flat condition and weighted Sobolev norms, we will review previous research on ALE Ricci-flat 4-manifolds. In particular, we present joint work with G. Chen, which extends the results of Biquard and Hein, offering refined expansions of harmonic forms and metrics at infinity. Utilizing techniques from b-calculus, we demonstrate a Fredholm framework that enables the construction and analysis of unique solutions to related differential equations.