Speaker: |
Raghu Meka (University of California, Los Angeles) |

Organiser: |
Prahladh Harsha |

Date: |
Wednesday, 19 Jul 2023, 16:00 to 17:00 |

Venue: |
AG-66 |

(Scan to add to calendar)

What is the largest value of $C$ such that for large enough $N$, every such set $S$ necessarily contains a 3-term arithmetic progression?

In 1953, Roth showed this is the case when $C$ is roughly (log log N). Behrend in 1946 showed that $C$ can be at most $exp(\sqrt(\log N))$. Since then, the problem has been a cornerstone of the area of additive combinatorics. Following a series of remarkable results, a celebrated paper from 2020 due to Bloom and Sisask improved the lower bound on $C$ to $C = (\log N)^{1+c}$ for some constant $c > 0$.

This talk will describe a new work showing that $C$ can be as big as $exp((log N)^{0.08})$, thus getting closer to Behrend's construction. Based on joint work with Zander Kelley (Univ of Illinois, Urbana Champaign).