Date: Friday, February 03, 2017
Location: 4088 East Hall (3:10 PM to 4:00 PM)
Title: Large colored sum free sets in finite vector spaces
Abstract: 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 sumfree 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 sumfree set, so bounds on colored sumfree sets are in particular bounds on sets without 3term arithmetic progressions. Until May of 2016, the best such bounds were of the form A^(1o(1)). Last May, Ellenberg and Gijswijt, building on work of Croot, Lev and Pach, proved bounds of the form A^c for c<1 when A is of the form (Z/p)^k. Robert Kleinberg, Will Sawin and I have constructed colored sumfree sets which meet these bounds to leading order. I will explain these exciting new bounds and our construction.
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Speaker: David Speyer
Institution: U. Michigan
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