September 13, 2023
TITLE: Instantons on Joyce’s G₂-manifolds

ABSTRACT: As 7-manifolds with special holonomy, examples of compact G₂-manifolds were first constructed by Joyce as resolutions of flat G₂-orbifolds. Later, Walpuski constructed non-trivial G₂-instantons over Joyce’s manifolds via gluing techniques. In this talk, I will first explain how to define a deformation invariant of G₂-orbifolds by counting flat connections, then describe the moduli space of instantons over certain non-compact G₂-manifolds that appeared in Joyce’s construction, with the aim to give a complete description of moduli spaces over some examples in Joyce’s list.