Hindmanʼs Conjecture over the Rationals

Ryan Alweiss, Princeton University
Fine Hall 224

We settle Hindmanʼs conjecture over the rationals, proving that for every coloring of the set of positive rationals by a finite number of colors and for every integer n>1 there are n numbers x_1,..,x_n so that all of them, all their subset sums and all their subset products have the same color.