Invited talk: Jacob Fox (Stanford University, USA) скачать в хорошем качестве

Invited talk: Jacob Fox (Stanford University, USA)

This is the video of the Invited Talk at the MCA 2021 (Buenos Aires) delivered by Jacob Fox on Tuesday July 20 at 14:45 (-3 UTC). Speaker: Jacob Fox (Stanford University, United States) Title: Subset sums, completeness and colorings Abstract: 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).