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Differential Geometry Seminar
$\mathbb{Z}/2$ harmonic forms, harmonic maps into R-trees, and compactifications of character variety
$\mathbb{Z}/2$ harmonic forms, harmonic maps into R-trees, and compactifications of character variety
Organizers
Speaker
Siqi He
Time
Tuesday, October 22, 2024 3:00 PM - 4:00 PM
Venue
A7-101
Online
Zoom 638 227 8222
(BIMSA)
Abstract
In this talk, we will explore the connection between the analytic compactification of the moduli space of flat $SL_2(\mathbb{C})$ connections on closed, oriented 3-manifolds defined by Taubes, and the Morgan–Shalen compactification of the $SL_2(\mathbb{C})$ character variety. We will discuss how these two compactifications are related through harmonic maps to R-trees. Additionally, we will discuss several applications of this construction in the analytic aspects of gauge theory. This is joint work with R. Wentworth and B. Zhang.