Discrete Math Seminar

The Rado graph is a fascinating object, very much like the rationals in many respect. We will first describe some basic properties of the graph and its automorphism group. Then we will identify some interesting groups of permutations containing the automorphism group of the Rado graph.

It became known, first probable due to a student of Todorcevic, that a metric space is oscillation stable if and only if it is approximately indivisible. I will give a very elementary proof of this theorem, discuss history of functional analysis, and then the framework within discrete mathematics in which such notions are naturally arising.

Using the Game of Morra as an example to compute expected payoff scenarios......

A chain in a poset is simply a (2-element antichain)-free subset of the poset, and an antichain is a (2-element chain)-free subset. So a few years ago I made the following attempt at generalization: for a given poset F, is there an integer c(F) with the property that every poset P can be coloured with c(F) colours so that every maximal F-free subset of P gets more than one colour? We will see the current state of affairs.

In this talk, we analyze the relationship between the structure of a graph and the eigenvalues a particular matrix representation of that graph. In particular, we focus on the Laplacian matrix and discuss classic results such as the Matrix-Tree Theorem (Kirchhoff's Theorem), and also introduce some new results.