A complete mapping of a group G is a bijection f : G → G such that the map x f(x) is also a bijection. Hall and Paige conjectured in 1955 that every finite group satisfying a certain necessary condition has a complete mapping; this was proved in 2009 by Wilcox, Evans, and Bray using the classification of finite simple groups. I will discuss recent joint work with Freddie Manners and Rudi Mrazovic in which we asymptotically count complete mappings using something like the circle method.
This talk relates to this arXiv paper.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
