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.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/6656