# On Szemeredi's Theorem with differences from a random set

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.