On the Geometry of $G_2$-Monopoles and the Donaldson--Segal Program
[HYBRID WORKSHOP] New Four-Dimensional Gauge Theories October 24, 2022 - October 28, 2022
Location: SLMath: Eisenbud Auditorium, Online/Virtual
$G_2$-monopoles
On The Geometry Of $G_2$-Monopoles And The Donaldson--Segal Program
$G_2$-monopoles are special solutions to the Yang--Mills--Higgs equation on (noncompact) $G_2$-manifolds, similar to the 3-dimensional BPS monopoles.
Donaldson and Segal conjectured that these gauge theoretic objects have a close relationship to the geometry of the underlying $G_2$-structure. Intuitively, $G_2$-monopoles with “large mass” are predicted to concentrate around coassociative submanifolds.
In this talk, I will introduce the relevant concepts to this conjecture, in particular, $G_2$-monopoles and coassociative submanifolds, in more detail. Then I will explain what the state-of-art is, with an emphasis on the work I have done (or planning on doing) with my collaborators.
This is a joint project with Gonçalo Oliveira, Daniel Fadel, Saman Habibi Esfahani, and Lorenzo Foscolo.
On The Geometry Of $G_2$-Monopoles And The Donaldson--Segal Program
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