Joint School of Mathematics and ACO Colloquium
Thursday, January 21, 2010 - 11:05
1 hour (actually 50 minutes)
The term Probabilistic Method refers to the proof of deterministic statements using probabilistic tools. Two of the most famous examples arise in number theory. these are: the first non-analytic proof of the prime number theorem given by Erdos in the 1940s, and the recent proof of the Hardy-Littlewood Conjecture (that there are arbitrarily long arithmetic progressions of primes) by Green and Tao. The method has also been succesfully applied in the field of graph colouring. We survey some of the results thereby obtained. The talk is targeted at a general audience. We will first define graph colouring, explain the type of graph colouring problems which tend to attract interest, and then explain the probabilistic tools which are used to solve them, and why we would expect the type of tools that are used to be effective for solving the types of problems typically studied.