March 1, 2022: talk by Dimitri Kanevsky (Google) on “A Non-Associative Moufang Loop of Point Classes on a Cubic Surface”

Video of the talk

The talk of Dimitri Kanevsky is devoted to an example of a non-associative Moufang loop associated to cubic surface. Such Moufang loops appeared in a Yu.I. Manin book about Cubic hypersurfaces, 1st Russian edition published in 1968. All previously known examples of Moufang loops associated to cubic hypersurfaces were associative and so Abelian groups as Abelian groups of elliptic curves, hypersurfaces of dimension 1. Moreover, H.P.F. Swinnerton-Dyer established that for non-degenerate and quite general cubic surfaces over local fields Moufang loops for these cubic surfaces are actually associative. In his book Yu.I. Manin stated a natural question more than 50 year ago. Do really exist non-associative Moufang loop of classes of points on cubic hypersurfaces? In his talk Dimitri Kanevsky gives the first example of this nature for a cubic surface.

This talk is also the first talk in mathematics which uses speech recognition technology. And the program for recognition was co-invented also by Dimitri Kanevsky.