Let A be an abelian group. A colored sum free set of A is a list (a_1,b_1,c_1), (a_2,b_2,c_2), ..., (a_N,b_N,c_N) of triples of elements of A such that a_i+b_j+c_k=0 if and only if i=j=k. Extremal combinatorialists aim to construct large colored sum-free sets, both because it is fun and because it has applications in the construction of fast matrix multiplication algorithms. Note that, if X is a subset of A with no three term arithmetic progressions, then the set of (x,-2x,x) for x in X is a colored sum-free set, so bounds on colored sum-free sets are in particular bounds on sets without 3-term arithmetic progressions. Until May of 2016, the best such bounds were of the form A^(1-o(1)). Last May, Ellenberg and Gijswijt, building on work of Croot, Lev and Pach, proved bounds of the form A^c for c Speaker(s): David Speyer (U. Michigan)