On the cap-set problem and the slice rank polynomial method
In 2016, Ellenberg and Gijswijt made a breakthrough on the famous cap-set problem, which asks about the maximum size of a subset of F_3^n not containing a three-term arithmetic progression. They proved that any such set has size at most 2.756^n. Their proof was later reformulated by Tao, introducing what is now called the slice rank polynomial method. This talk will discuss Tao’s proof of the Ellenberg-Gijswijt bound for the cap-set problem, as well as further applications of Tao’s slice rank polynomial method.