Izar Alonso, Rutgers University
Gauge Theory on hyperkähler manifolds
$H$-instantons are a distinguished type of connections on Riemannian $n$-manifolds, as they are generalizations of anti-self-dual connections to manifolds of dimensions greater than 4. Examples of $H$-instantons include primitive Hermitian Yang--Mills (pHYM) connections, $\mathrm{Spin}(7)$-instantons,which have been of great interest in the recent years, and the less studied $\mathrm{Sp}(n)$-instantons. In this talk, I will describe $\mathrm{Sp}(2)$-instantons on hyperk\"ahler $8$-manifolds and their relations with other gauge-theoretical objects. I will then describe the construction of examples of $\mathrm{Sp}(2)$-instantons,pHYM connections, and $\mathrm{Spin}(7)$-instantons with symmetry on the manifold $T^* \mathbb{CP}^2$with the Calabi hyperk\"ahler structure. This talk is based on arXiv:2508.17119.
MC 5417