Abstract: I will describe a physically-motivated conjectural approach (developed with Shamit Kachru and Arnav Tripathy) to the construction of hyperkahler deformations of $(\mathbb{R}^{4-r} \times T^r)/\Gamma$ with $0\le r \le 4$, where $\Gamma$ is a finite group, as well as recent work with Arnav Tripathy which proves some of these conjectures. This generalizes Kronheimer’s construction of ALE manifolds in the $r=0$ … Read More