Invited talk

Tuesday, July 20, 14:45 ~ 15:45 UTC-3

Subset sums, completeness and colorings

Jacob Fox

Stanford University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk, we discuss novel techniques which allow us to prove a diverse range of results on representing integers as subset sums, including solutions to several long-standing open problems in the area. These include: solutions to the three problems of Burr and Erdős on Ramsey complete sequences, for which Erdős later offered a combined total of \$350 for their solution; analogous results for the new notion of density complete sequences; the solution to a conjecture of Alon and Erdős on the minimum number of colors needed to color the positive integers less than $n$ so that $n$ cannot be written as a monochromatic sum; the exact determination of an extremal function introduced by Erdős and Graham on sets of integers avoiding a given subset sum; and, answering a question reiterated by several authors, a homogeneous strengthening of a seminal result of Szemerédi and Vu on long arithmetic progressions in subset sums.

Joint work with David Conlon (Caltech, USA) and Huy Tuan Pham (Stanford University, USA).

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