  In this short note, we present some evidence towards the existence of an
algebra of BPS $G_2$ instantons. These are instantonic configurations that
govern the partition functions of 7d SYM theories on local $G_2$ holonomy
manifolds $\mathcal X$. To shed light on such structure, we begin investigating
the relation with parent 4d $\mathcal N=1$ theories obtained by geometric
engineering M-theory on $\mathcal X$. The main point of this paper is to
substantiate the following dream: the holomorphic sector of such theories on
multi-centered Taub-NUT spaces gives rise to an algebra whose characters
organise the $G_2$ instanton partition function. As a first step towards this
program, we argue by string duality that a multitude of geometries $\mathcal X$
exist that are dual to well-known 4d SCFTs arising from D3 branes probes of CY
cones: all these models are amenable to analysis along the lines suggested by
Dijkgraaf, Gukov, Neitzke and Vafa in the context of topological M-theory.
Moreover, we discuss an interesting relation to Costello's twisted M-theory,
which arises at local patches, and is a key ingredient in identifying the
relevant algebras.
