When we take a moment to consider mathematics and its distinct areas of study, we often classify it into two groups: continuous and discrete. The focus of this talk lies in an area formed by the union of combinatorics, which lies at the heart of discrete mathematics, and topology, which is commonly described as the study of continuity.

Whilst the general area of combinatorial topology gave way to the more versatile algebraic topology in the early 1940's, there remain problems of a topological nature which can be more readily stated and proven in combinatorial terms. In this Discussion Group, Owen Daniel will first state and prove Sperner's Lemma, a purely combinatorial result, which will then be shown to be a surprisingly versatile tool culminating in a proof of the Brouwer Fixed Point Theorem, a classic problem of algebraic topology.

So come along on Thursday to be guided through a meandering stream of mathematics: the pace will be gentle, and as such is suitable for all maths students. It is also an excellent example of what is suitable for a second year essay, as much of the talk is based on Owen's essay, available here.

After the talk, as usual, we triangulate our way to the pub!