On Szemeredi's Theorem with differences from a random set

Speaker: 

Daniel Altman

Affiliation: 

University of Oxford

Date: 

Wed, 11/12/2019 - 2:00pm

Venue: 

RC-4082, The Red Centre, UNSW

Abstract: 

Szemer\'edi's theorem says that subsets of the integers with positive density contain $k$-term arithmetic progressions ($k$APs). We investigate the probability threshold for which $k$APs are guaranteed when the set of allowed common differences in arithmetic progressions is a random set. In particular, we will show that this threshold in the finite field setting is larger than the conjectured threshold over the integers.

School Seminar Series: