Everyons who is interested is welcome to attend the lecture of Dion Gijswijt, with the title 'Asymptotic upper bounds on progression-free sets in Z_p^n'.
Abstract:
We show that any subset of Z_p^n (p an odd prime) without 3-term arithmetic progression
has size O(p^{cn}), where c := 1 − 1/(18 log p) < 1. In particular, we find an upper bound of
O(2.84^n) on the maximum size of an affine cap in GF(3)^n.
