Group actions on exotic smoothings of $\mathbb{R}^4$

It has been known for more than three decades that there are uncountably many diffeomorphism types of smoothings on $\mathbb{R}^4$, so in some sense there is a shortage of diffeomorphisms. However, nothing has been known about the self-diffeomorphisms of such a manifold up to smooth isotopy, except that there is only one (preserving orientation) for the standard smoothing. This talk will cover a recent breakthrough in the matter.