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Event Series Event Series: Colloquium

Strong bounds for arithmetic progressions

March 4, 2024 @ 4:30 pm - 5:30 pm

Colloquium

Speaker: Raghu Meka (UCLA)

Title: Strong bounds for arithmetic progressions

Abstract: Suppose you have a set S of integers from {1,2,…,N} that contains at least N / C elements. Then for large enough N, must S contain three equally spaced numbers (i.e., 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 much closer to Behrend’s construction. Based on joint work with Zander Kelley.

Details

Date:
March 4, 2024
Time:
4:30 pm - 5:30 pm
Series:
Event Category:

Venue

CMSA Room G10
CMSA, 20 Garden Street
Cambridge, MA 02138 United States
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Phone:
6174967132