SMS scnews item created by Giles Gardam at Thu 13 Sep 2012 1123
Type: Seminar
Distribution: World
Expiry: 20 Sep 2012
Calendar1: 13 Sep 2012 1300-1400
CalLoc1: Carslaw 351
Auth: gilesg@bari.maths.usyd.edu.au

# SUMS: Menzies -- Van der Waerden’s theorem on monochromatic arithmetic progressions

Speaker: Max Menzies (Cambridge undergrad)

Abstract:
Suppose you have the counting numbers 1,2,3,... and you colour each
number (a point on the number line) red or blue. There are many weird
and wonderful colourings that exist, but one aim of combinatorics (in
particular Ramsey Theory) is to find method within the madness.

So one question that can be asked is: can you always necessarily find
an infinite monochromatic arithmetic progression? That is too much to
ask for, as there is not always an infinite mono AP.

Van der Waerden’s theorem asserts the next best thing: that there are
always arbitrarily long finite monochromatic APs, no matter the