# Jacob Fox "Subset sums, completeness and colorings"

**Jacob Fox** from Stanford University will
give the talk "Subset sums, completeness and colorings" on the labs' Big Seminar.

Password: first 6 decimal places of $\pi$ after the decimal point

You can also write to Alexander Polyanskii (alexander.polyanskii@yandex.ru) or to Maksim Zhukovskii (zhukmax@gmail.com) if you want to be added to mailing list.

**Abstract:**

We develop novel techniques which allow us to prove a diverse range of results relating to subset sums and complete sequences of positive integers, including solutions to several long standing open problems. These include: solutions to the three problems of Burr and Erdös on Ramsey complete sequences, for which Erdös later offered a combined total of 350 analogous results for the new notion of density complete sequences; the answer to a question of Alon and Erdös 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 Erdös and Graham and first studied by Alon on sets of integers avoiding a given subset sum; and, answering a question of Tran, Vu and Wood, a common strengthening of seminal results of Szemerédi-Vu and Sárközy on long arithmetic progressions in subset sums.

Based on joint work with David Conlon and Huy Tuan Pham.

## Watch the video:

Everyone is invited to attend. The language of the lecture is English. The event is aimed at master and graduate students, as well as researchers in the field of combinatorics.