In the introduction to mathematical seminars these days, one often hears defensive arguments to convince the audience of the real-world applicability of the mathematical results to be presented. A few generations ago, mathematicians of the English tradition in particular, proudly announced that their mathematical results were 'pure' and without any sullying real-world applications. Both points of view are quite reasonable within their particular cultural contexts. However, I would claim that, apart from mathematical modeling and other branches of mathematics that exist solely for real-world applications, the distinctions between `pure' and `applied' mathematics is entirely artificial. To support this claim, I will in this talk present three nice dual identities from combinatorics and coding theory: Greene's Theorem on posets, the MacWilliams identity for linear codes, and a new and intriguing identity concerning graphs and more abstract combinatorial objects. Each of these results could well be considered to be quite abstract and thus `pure'. However, I will show how the abstract theory behind these results lies closer to real-world applicability than one might first imagine. In addition, I will describe some of the newly-discovered connections between the theories underlying the three duality identities.


Dr. Thomas Britz

Research Area

Pure Maths Seminar




Tue, 03/08/2010 - 12:00pm