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# 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

October 27, 2022 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Ákos Nagy (University of California, Santa Barbara)
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
• $G_2$-monopoles

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Video

#### On The Geometry Of $G_2$-Monopoles And The Donaldson--Segal Program

Abstract

$G_2$-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.