4pm - 5pm
Wednesday 24 October 2018

Sets of integers containing (almost) arithmetic progressions

Jonathan Fraser from the University of St Andrews will be speaking.

Free

Thomas Telford building (AA), floor 4, room 22
University of Surrey, Guildford
University of Surrey
Guildford
Surrey
GU2 7XH
back to all events

This event has passed

There's no need to book your place, please just show up on the day.

Abstract

An arithmetic progression is a finite sequence of real numbers with a constant gap sequence. For example, 1,3,5,7 is an arithmetic progression of length four (there are four terms) and gap size two (the gap between any two consecutive terms is two). Given a set of integers, it is natural to ask whether or not it contains arithmetic progressions of certain lengths.

The Erdos conjecture on arithmetic progressions says that if the reciprocals of a set of positive integers form a divergent series then the set should contain arbitrarily long arithmetic progressions, that is, for all k, there is an arithmetic progression of length k somewhere inside the set. The celebrated (and deep) Green-Tao Theorem is a special case of this conjecture. Jonathan will discuss a simple approach to this type of problem where one can show that such sets get arbitrarily close to arbitrarily long arithmetic progressions.

Visitor information

Find out how to get to the University, make your way around campus and see what you can do when you get here.