# Jacob Fox “Subset sums, completeness and colorings”

June 18, 2020
19.00 MSK (UTC +3)

# 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.

The talk will be held in zoom
Meeting ID: 279-059-822
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.